While it is true that the Khilafah in their vast conquests and acquisition of ancient knowledge did result in an enormous growth of technology and innovation and in some cases economic growth (Baghdad & Spain), but the question of is Islam or even an all encompassing Khilafah needed for greater innovation or economical growth is not certain and it is quite uncreative to say that only the Khilafah could do this and that the Khilafah did not cause it's own problems and actually cripple itself while innovating at the same time, often nullifying any real advance.
First let's define why the Khilafah experienced the huge growth in innovation that it did. The innovation was caused by a surge of conquest by the Rashidun that saw the acquisition of the Roman/Hellenic Middle East and the lands of Persia and Iraq, this gave a desert Bedouin people an enormous empire with a huge tax base and almost the entirety of the Western worlds ancient literature (preserved by Byzantium and Sassanids). Thej most of the subjects in Iraq and the Levant where Semitic speakers, who easily adapted Arabic and easily translated everything for the Arabs into Arabic, thus giving a people who previously had no books (except the Quran and a rich oral tradition) an enormous array of books easily readable and taught to them by Syriacs who had a long history of knowledge. The people where then inspired and a surge of innovation began.
With this said, the Khilafah did not have a clean streak and by no means where perfect and in fact hindered other venues of innovation in the world by their constant conquest and other backward practices. First of all, despite conventional beliefs, the Sassanid and Byzantine empires where not some sort of backwater that the Khilafah removed from the Middle East, and in fact it was simply the remaining and slowly returning status quo of the Roman and Hellenic period, basically the recovering borders of the ancient Hellenic world, with the Europeon world centered around the Mediterranean and the Persian world focused on Iraq and trade towards India and China. The Khilafah removed this creation by crushing both notions, basically destroying the old Hellenic Middle East, opening the Red Sea and the Persian Hulf as the dominant trade zones for the Levant and Persia rather than the Mediterranean and China respectively. So from the start it is possible that without the Khilafah destroying the Mediterranean exchange and the Hellenic worlds dominance of Europe that Europe would have slowly come around perhaps even much quicker and the hope of Roman Empirium would still be alive; and in Persia dynastic succession would continue in China like cycles and the status quo would remain until an upstart people destroy it.
Then the topic of the effect of the Khilafah on the growth of Byzantium and all neighboring kingdoms is known. The Khilafah due to Shariah, was unable to take Muslim slaves or take slaves out if any people who paid Jizya tax, thus the Khilafah was faced with a problem how would they continue furnishing their people with slaves (that was a cultural norm in Arabia and in nomadic cultures) if everyone in their territory (unless they refused to pay Jizya, Armenia) where all forbidden to take. What was the solution? War, and constant war at that Baqqiyyah Wa-Tattamadad (remaining and expanding) was the policy of the Umayyads and the Abbasids, this led to near constant war against Byzantium for islands and Italy, retarding their economic and innovative growth significantly. As well, the Khilafah's effect on Africa was huge as well, the vast taking of Bantu (Zanj) slaves and on a huge scale led to depopulation of East Africa and the crippling of the Aksumite/Ethiopian kingdoms draining them of people and pushing them from the coast farther into the interior. So without the Khilafah it is very possible to see a far more advanced and populated East Africa not drained from slavery. As well, the practice of slavery opposed to urbanization is never good and in many cases caused the downfall of the Arab Khilafahs. By promoting slavery in a rural nomadic lifestyle the city was neglected (opposed to the older Hellenic and Persian world). These slavery practices where defended by numerous high level Arab philosophers during the Abbasid and Umayyad eras. These practices led to massive revolts (also spurred by religious fanaticism against a decadent Khilafah) such as the Zanj rebellion and the many Berber revolts, these weakened the Khilafah to the pint of subjugation to Turkish slaves who relied upon rather than the Arab relying upon himself. We know what happened afterwards a general decline in Middke Eastern innovation until the Ottoman Empire.
Then we get to India where the Khilafah and caused further chaos by attacking Pakistan and the interior for slaves, this further decentralized India and stifled economic and innovative growth by making them have to constantly fight a nation who warred mainly just to take slaves periodically, this would change with the Ghaznavids who actually attempted to conquer India, but that is another story, on how that hurt India further and crippled their economic growth until the Mughal Empire stopped waging war just for slaves and people to force Jizya on, but to actually rule.
Further on economics is the problem with the Khilafahs innate love for the Bedouin and the desert nomadic lifestyle. These ideals where in deep consrast to the settled and urban Hellenic peoples and Persians. This would turn into the vast use of the goat and camel upon the Middle East and the deteriorated use of the wheel due to a lack of perceived need, the Arabs saw no need for wheels whenever their grandfather used a camel to carry his stuff from Mecca to Jiddah, also try using a wheel cart through the rural areas of the Nejd lol. This would leed further to the expansion of Bedoiun throughout the nation removing farmland (North Africa) who brought goats, goats who once used on the fragile North African soil who had already deteriorated since Rome, led to a catastrophe and the increased expansion of the Sahara that's growth might have been averted by agricultural countermeasure from Byzantium. These difficulties would make the Middle East ecomically unprepared for the age of imperialism.
Further while areas like Al-Andalus where scientifically amazing and economically sound (for the time not in the long) where still inwardly crippled by the same thing that hurt Mali, Ghaznavids, Crimea, Barbary states, etc. That problem was the continued use of ineffective taxing methods and in many cases refusal to take taxs from unbelievers because a person who refuses to pay Jizya is immediately a target for slavery, hence in Iberia the Khilafah in many cases allowed Christian states to live or not take taxes from them so whenever they needed to they could just take slaves. This was seen dramatically in Mali, where until the rise of the Songhai and Sokoto, the Emirates refused or just didn't try to assimilate its people so they would have a steady supply of slaves and since pagans rarely pay Jizya, everyone was free game.
Then the elephant in the room is the perceived decadence and Bidaa of these Khilafah (mainly Abbasids) by its subjects who rebelled in the form of anti noble Arab attacks led by Khawarij/Shurha and the Shia backlash to mistreatment by the Khilafah towards them and a hope to come out of Taqqiyyah. This led to massive revolts further draining a already drained land.
To clear this up I want to say I am not taking a shot towards Islam in any way and am only combating romanticism and the lack of critism of some of the Khilafah's dubious economic policies and I never referred to Islam as the reason for any of these problems.
Sorry for spelling errors, I don't feel like proofreading this atm lol.