I'm going to put forward an idea I rarely see discussed but think may have some merit.
There is a legacy of a great Mediterranean superpower- Rome- that tied together everyone in a massive civilization. We can call this analogous to China.
But there is another legacy- a far older one. Stretching back to the days of Ancient Assyria, a single power has united much of Mesopotamia and the Eastern Mediterranean into a superpower of its own. There is a long history here, continued by the Persians and even Alexander's Empire. This idea runs directly counter to the idea of a great Mediterranean Empire- the two cannot easily coexist.
Both ideas are supported by the geography of the region, which encourages each to unite. Both Mesopotamia and the Eastern Mediterranean facilitate easy transportation and communication, allowing an Empire. Both have cultures set to do just this, and structures set up that allow it.
The two ideas clashed repeatedly. Look no further than the Eternal War- a Roman Empire under Justinian and successors that yes, struggled with barbarians and plague, but was never threatend by them on the level of the Persians. Then, even after defeating them, a new empire formed in the Arabs and came to realize the Persian ambition of dominating the Eastern Mediterranean, while a remnant of the Roman idea held out in Byzantium.
There is no such analogy in China. There is one great state with one great history and no great rivals. And I would like to put forward the idea that this is the reason China stayed united, and Rome did not. Yes, the migration of nomadic and tribal groups were a constant threat. But they never were a true cultural rival to the Romans. Only due to the intervention of first the Persians and then the Arabs were the very powerful remnants of the Romans- who otherwise stood a good chance to reunite the entire Mediterranean- distracted and stopped, which eventually allowed the former barbarians to begin developing their own cultures and traditions.
While I think that you are using some good reasoning, I would have to disagree with you on some matters here and clarify things relating to Chinese and Near Eastern history, culture and geography.
1. A Mesopotamian 'Empire:'
While the geography of Mesopotamia may seem to an onlooker in the recent era to be a place that is both easy to unite on account of flat terrain and rivers, this is not necessarily the case bore out in fact. You spoke of the Assyrian 'empire' and its formation of an empire and that this was in a sort of succession of unification in Mesopotamia. One matter that must be clarified, this process of unification in Assyria was far, far more difficult that what is assumed and geographic features played little to no role in aiding Assyrian expansionism in the region. Assyrian expansion was further unaided by riverways, as the rivers by the time of imperialistic Assyria during the reign of Shalmaneser I (1273-1243 BCE) were contested by multiple powerful realms; the Kassite kingdom of Karduniash ruling from Babylon, the Mitanni realms based from Washukanni and then the many decentralized vassals or tribal states affiliated with the Hittites. Assyria would manage in the later realm of Shalmaneser I to conquer Mitanni and then under his son Tukulti-Ninurta I (1243-1204 BCE) asserted a brief hegemony over Karduniash to the south (Babylonia). However, these conquests were quickly overturned, not just once after the death of Tukulti-Ninurta I but also under the many periods of Assyrian hegemony where local people broke from Assyrian rule rapidly. During the reigns of the following Assyrian kings, we have the collapse of the Assyrian kingdom outside of its heartland in Assyria: Tukulti-Ninurta (1243-1204 BCE), Assur-Resh-Ishie (1132-1115 BCE)/Tiglath-Pileser I (1115-1076 BCE), Adad-Nirari III (811-783 BCE), Tiglath-Pileser III (745-727 BCE), Shalmaneser V (727-722 BCE), Sargon II (722-705 BCE), Assurbanipal (669-631 or 627 BCE). This ebb and flow describes an empire which is, without a doubt, unstable in terms of its consistent grasp on exterior territories.
All people agree that the Assyrian kingdom had an issue with stability outside of its core heartland but the question is why is this the case? In order for us to understand this matter, it is important to consider what the Assyrians themselves thought, which is an important endeavor. Assyrian royal dogma was that pastoralist peoples were not truly human, especially those pastoralists that resided outside of the dominion of Assyria. Assyrian view was clear-cut, all humans must exist withing the 'Bronze Age framework' that is submission to a monarch, a complex centralized temple system, intensive agriculture along river ways, intense state management of irrigation networks and adherence to a sort of devoted polytheism. Attempts were made to enforce agriculture upon their domains constantly through the banning of fruit trees, the forcible deportation of pastoral people, re-education through assimilation programs and intense irrigation funding by the state. Intense effort was made to correct what was seen by Assyria as a divine evil of pastoral nomadism and 'the men who act as ibex,' and more than most states that have existed in pre-modern times, Assyria was a hyper-centralized state with all the necessary organs to do so. Here we see that the Assyrians, while possessing a cultural-religious aversion to the tribalistic peoples of the Middle East, their reasoning derives from a political goal, an understanding of population management.
The pastoralist peoples were noted by Assyria as possessing deep tribalistic loyalties that override the submission to the divine cult of Assyria and the state itself, an organ of the Great Gods of the Lands. Pastoral peoples held deep familial connections that weakened state loyalties, they were mobile and hence able to avoid state officials, they were warlike and could devastate sedentary militia (hence the creation of professional and noble elite armies in Assyria), and finally their economic practices implied a counter to the Assyrian irrigation networks which relied on sedentary farming and not stripping the land with goats, sheep and other cattle alongside seasonal farming and date collection (which destroyed the Assyrian farmlands and when Assur-Dan II (934-911 BCE) begins his reconquests, he laments the pastoral ibex destroying the farmlands with their goats, cattle and sheep). We see thus the reason for Assyrian instability in control, at least the most principle one...
Wherever Assyrian hegemony stretched in the Middle East, they were harried, not by external foes always, but by a fifth column of unmanageable warlike pastoral tribes that, taking advantage of the arid climate for which they were more well adapted to than the Assyrians (and by extension their entire Bronze Age Mesopotamian cultural complex), resisted, upturned and destroyed Assyrian hegemony wherever they existed. Cities in Syria that otherwise were submissive found their allies in these tribes that beckoned for war against the Assyrians, the otherwise rich and fertile Babylonia was paralyzed by tribal infighting and dominion outside of the cities and in the interior of the region (away from rivers), and the mobile pastoralists could outmaneuver the Assyrian war machine. Assyrian efforts to maintain their empire was in spite of an existing geography, which, not only supported pastoral nomads, also directly countered the notion of a centralized empire by disrupting the economic, cultural and societal expansions needed for a centralized sedentary empire and instead the geography sired a more popularly aggressive tribalistic pastoral group(s).
2. Geography of an Empire --- Middle East
As mentioned previously, the creation of stable centralized empires is made difficult where we have certain geographic features, this is always agreed upon. From the Assyrian standpoint, this holds true, as the arid climate preferred the creation and propagation of pastoral people groups who, by their cultural and economic lifestyle, could not be assimilated to the sedentary imperialistic Assyrian state structure. However, does this situation hold true across other empires that would develop in the region? The answer is an emphatic yes, but these empires would progressively adopt decentralized methods to try and assuage the geographic tendencies of the Middle East towards disintegrating effective state power.
All empires that existed with a base of operation in the Middle East showed signs of weakness in relation to the geography, which, though flat and navigable, also promotes lifestyles that ultimately run counter to imperialistic ambitions (and to a far greater degree than in Europe!). The Achaemenid empire had to combat frequent rebellions from the Aramaic/Arab tribes across the Middle East and maintained stiff garrisons in order to keep the order in addition to decentralizing the empire where necessary so as to limit problems (and a large percentage of the population in the Mid East under Achaemnid rule likely never paid taxes or dues or any kind of regulatory amount due to the mobility of much of the populace). The Arsacid hegemony (Parthian empire), was very decentralized and ruled the Middle Eastern lands through proxy and series of tributaries, both on account of the nomadic descent of the Arsacid themselves but also a realization of the geographic and cultural situation of the Middle East. Sassanid centralization was attempted and succeeded in part, but Sassanid Mesopotamia was constantly hampered by Arab raiders, Arab rebels, Arab tax evasion, depletion of farmlands and its conversion to pastures and this is not mentioning the high levels of decentralization in Iran itself under the Great Houses. The varied iterations of the Islamic Caliphate were plagued by pastoral nomadism which contributed to rebellions, sectarian conflict and ultimately, the collapse of the Abbasid hegemony. Subsequent states in the Middle East were less large or utilized a sort of high level of decentralization in relation to large swathes of the population, but in the same vein, these regions suffered consistent problems related to the geography promoting nomadic or pastoral lifestyles which in turn played a major role in disintegrating imperialistic ambitions.
In brief, the geography of the Middle East does not suggest a unification of powerful empires, but instead suggests a difficult situation for long term empires, unless they develop from a nomadic background and or have a very particular method to maintain stability within the region. Thus, the region of the Middle East and its geography does not lend itself towards imperialism, but instead towards state fragmentation and the creation of mini-tribal domains and or city states between desert and riverways.
3. Sassanid goals and Succession with the Abbasid or Umayyad Caliphates as geopolitical terms
The Sassanid empire, generally, aside for the dreams of a few Sassanid monarchs such as Kavadh (488-531) and Khosrau II (590-628) do we see the concept of 'dominating the Eastern Mediterranean' or 'restoring Persian borders.' Rather, the Sassanid modus operandi was exactly the same as that of the Arsacid before them: raid the west, defend/expand in the east. Geopolitical concerns work both ways, and the Sassanid empire was more harried to the east than to the west and the west was utilized as a zone of loot for which the Great King could gain glory and more importantly, distribute loot to the Great Houses whose exalted royal leadership viewed as their birthright. Note Shapur I (240-270) and Shapur II (309-379) both, despite gaining huge victories over Rome in the field and essentially having the means to conquer Syria then and there, essentially just formed baggage trains of loot, dismantled forts and then returned in haste to their lands acting as if it was a grand victory. The reasons for this is clear; the Great Houses which monopolized enormous power in the affairs of Eranshahr had little interest in the situation in Syria except that it could grant them booty and glory. Rather, the Great Houses had their eyes turned east towards the varied number of easterly threats and acquisitions, the Kushan empire, the Kidarites, the Alchon huna, the Hepthalites, the Celestial Turks and so on and on. Threats emerging from the east and the petty particularism of the Great Houses limited any idea of ruling Syria or the Levant to develop as an official policy of the Sassanid empire except in its late and declining phases where the bond between the Great Houses and the Sassanid court had all but died. Western perceptions of the geopolitical role of the Sassanids derived ultimately from propaganda developed and curated by the Greco-Roman world of a great oriental threat, but in reality the threat of the 'orient' was relatively mild, whereas the real threats existed internally and or to the north where Roman meddling created more militaristic societies and increasingly more sophisticated cultural traditions in threat to Rome amongst the Germanic and Sarmatian peoples.
The Arab imperial complexes called the Umayyad and Abbasid caliphate formed a totally different geopolitical and cultural iteration as the Iranian powers. These Arab realms and their expansion was one of a victory of the tribalistic and pastoral populaces over the settled sedentary and more centralized empires of the region. Islam itself promoted a decentralized governance and freedom of movement for the Arabs, combining this with economic success of Arabs that is aided by Sharia law, the Arabs quickly became a majority across the region. Arab victories militarily thus heralded economic, cultural and societal changes that were a long time coming but had been halted by governance by exterior empires such as the Sassanid or the Roman empires. Arab rule amounted to the expansion of a new order of the regions that they touched, one upheld by decentralized governance and an expansion (perhaps inadvertently) of the Arab pastoralist economic and social pattern, alongside the development of city states which act as way stations for these moving tribal populaces. Certainly, the Romans could not truly pinpoint or recognize the reason Islam and its rapid expansion was so successful and popular and hence they double-downed on their existing propaganda of a great oriental threat.
As an addendum, it is important to note the difference in imperialism of the Arabo-Islamic states and that of the Sassanid empire. Sassanid kings were Great King of Kings, rulers of the whole world, universal monarchs and their rule was justified by an aura of kings which was bestowed upon them by heaven. Their empire was defined not by culture, religion, common values or such, but overall submission and orbit around this King of Kings. In a sense, the Eranshahr was a form of Middle Kingdom likened to China, with the same kind of exterior-barbarian dichotomy. Sassanid universal dominion was also not something to be truly enforced externally, but rather was a point of internal stability and propaganda as 'world rulers.' Hence, Sassanid monarchs were at peace with ceremonially ruling the entire planet by having effigies of other lands created and made to prostrate to the Great King, which in turn it was assumed metaphorically placed the entire lands under the great King (similar rituals were practiced by the Assyrians). Abbasid rule by comparison was the opposite. Islamic universal empire is based less around the monarch as a factor in unification but rather about the unification around 'sharia law.' Islamic scholars of the past were clear, dar al-Islam is where the Sharia is enforced and not necessarily that placed where the Caliph or monarch rules. As such, Islamic hegemony as it developed was one where we have an expanding metaphorical or unseen realm of sharia law within Islam that in turn has aspects and benefits to the people who adopt it and this was ultimately the goal and ambition it would seem of the Islamic movement. Abbasid caliphs attempted to change this situation but their attempts were for naught as the Abbasid hegemony rapidly collapsed after only a century of attempting to develop a universal monarchy-like system.
4. Lack of competition as a reason for Chinese continued empire.
Until the Great Qing, the Chinese geopolitical entity was always arrayed against heavy competition and competing imperial designs. Contrary to popular view that China essentially sat upon a hill without competition in perpetual bliss, is a development and perception gained from the real status of the Great Qing who, through innovation ideologically and military prowess, managed to subdue the western and southern barbarians across Asia and subdue competing political and imperial claims. Chinese notions of supremacy derive from their perceived status as the developers of a harmonious civility within a Middle Kingdom enunciated in the Confucian classics and their commentaries, which do not illustrate the real status of the exterior peoples to China, but rather speak to the internal propaganda of thinkers in the Spring and Autumn Period or the Warring States Period. Confucius and his successors like Mencius and Xunzi, believed that China had declined from a supposed period of harmony, utmost etiquette and civility and the foreign barbarian was used as a counter to this created ancient Chinese custom and ritual that was displayed in the Rites of Zhou. This comparison to foreign barbarians would also be a means by which to convince local Chinese feudal lords of their ideals, for not being Confucian was to emulate the foreigners, who, in the xenophobic culture of China at the time, was a serious slight.
Rather, China had serious opposition to its exterior. The Confucian concept of a passive Middle Kingdom that develops a harmonious interior of inward perfection and practices wu-wei (active passivity) in foreign diplomacy would be counteracted by many different new notions of empire consistently across Chinese history. The nomadic empires of the steppe developed uniquely in the region as a competing universal empire to that of the Chinese Middle State, and one that was successful at opposing it. Xiongnu, Rouran, Celestial Turks, Qara-Khitan, Jurchen Later Jin, the Mongol empire(s), and finally China itself was submerged or otherwise morphed into the universalistic ambitions of the Aisin Gioro clan whose empire was that of the Great Qing, something both Chinese and yet something totally different entirely otherwise. Tibetan imperialistic claims also for a period challenged and outdid the Chinese, Goguryeo of Korea was able to do so and Japan at various periods combatted with Chinese notions of the Middle State. Excluding from this was the recalcitrant cultures who resisted Chinese hegemony in both economic, cultural and military affairs, such as the Tocharians (who created their own geopolitical model of city state alliances that had a symbiotic relationship with powerful steppe universal empires such as the Celestial Turks and Rouran). Let us discuss slightly in depth what I mean....
We could argue the imperialistic dominion of China to have reached its pinnacle (excluding the Great Qing) during the Great Tang, whose imperial gains extended furthest and who held very close to Confucian dogma of the Middle State and notions of superiority of Chinese culture and civility. Great Tang power began on rickety legs as the Great Tang began as a tributary and vassal to the universalist Celestial Turk empire which ruled most of the steppe at the time. Successful divide and conquer strategies and effective military campaigns would allow the Tang to dismantle the Eastern Turks and wage a continuous war with the Turkic successors who consistently attempted to either ingratiate themselves to Chinese order or recreate and the prior situation of a universal nomadic steppe empire ala the Xiongnu or the Celestial Turks. Tang success in the region however was very short term and rapidly the Tang found themselves assailed from the southwest by the Tibetan empire which, formed a counter imperialistic concept and hegemony, calling themselves equals to China. Likewise, Chinese vassals in the Tarim were treacherous and rebelled constantly and attempted to form netowrks of alliances with their neighbors and or play the varied empires against each other. Tang also had serious competitors in Goguryeo in Korea-Manchuria and Japan (which at the time exerted inordinate power over southern Korea and whose pirates raided the coasts of China).
The Tang would have a two-fold strategy in dealing with exterior opponents. Central court policy was to 'educate' the exterior barbarians in Confucianism and in civility and that with this education, these people would eventually, indeed inevitably integrate and submit to the sage-king, the Son of Heaven ruling from Chang'an. Such pretenses woudl be very poorly received and instead, Chinese education of exterior peoples would lead to these people creating counter narratives to Chinese hegemony and developing their own version of the Middle Kingdom (such as Japan, Goguryeo, Tibet, Dali [Yunan region]) and then re-enforcing the universalistic ambitions of the nomadic steppe empires that competed with the Chinese over the northern and western frontiers. Not getting too deep into the weeds of the Tang geopolitical strategy in East Asia, the Tang would not gain ultimate victory and would instead be subjected to an all encompassing defeat at the hands of the competing imperial systems of the Uyghur steppe empire and the Tibetan empire. Tang policy in lieu of this would create complex ways of admitting equality with other states around them without it directly harming their internal stability and would double-down on their wu-wei policy of passivity, and adopt a policy of 'turn barbarian against barbarian,' which was ultimately an admission of inability of China to combat these competing imperial systems. Later Chinese states would either do as the Tang did, such as the Song or they would do as the Ming did and ignore the exterior world so far is it came to competition and instead focused on 'cultivation of harmony.' However, even during the Ming, imperial entities emerged to compete with the Ming, namely the nomadic Oirat horde and its pretense at a revived Mongol empire, the Manchu later Jin (to become the Great Qing) and the Japanese. Ming ignorance of the exterior world was not to say that the Ming did not have competition, but only that the Ming and their diplomacy was built around denying what actually existed around them and hence the blindness of the Ming central court to the terror that befell Korea when the Japanese invaded it.
Therefore, there must be a different and more enigmatic reason for the unification of China continuously that has to do with more random and chance developments than in geopolitical competition.
Tang strategy in this field of combat of geopolitical