the Gothic wars in Italy completely destroyed the peninsula for 30 years and then later alienated the population who slowly abandoned the Roman identity for a more bell-like one, to give you an example Belisarius at the beginning when it was thought that the war would not last long was acclaimed as hero, but then with the Goths reorganizing themselves and the Romans stalling due to few soldiers the war got worse, (the twice destruction of Naples and the continuous changes of control of Rome did not help the Romans to be loved, not to mention the treatment to the popes of the period (one imprisoned and the other killed) by those who the more time passed the more they were seen as invading Greeks from Rome upwards at least. Also the fact that until the last years of Theodoric the great Italy was the Roman Germanic kingdom with more continuity with the Late Imperial period it didn't help in that because many people could compare the earlier with the present period is l the difference was noticeable (even the use of the Greeks in key posts of the reformed government ( in particular Narses much hated by the population for his abuses )in place of the natives did not do much to appease spirits, emblematic was the letter sent to Justinian by the Roman senators to stop the war and keep the city under Ostrogothic control should make you think.
P. s.
I write it with knowledge of the facts, I am Italian this piece is studied a lot at school because it is one of the main moments in the formation of our regional identities it is the first step in abandoning the Roman one, together with the arrival of the Lombards it is the consequent split of Italy into 2/3 areas of influence: Lombards, Eastern Romans (from now on call Byzantines) Papacy + Franks.
Even the fact that when the emperors showed up in Italy ( only two have done so in at least 250 years or so, namely Pochas and Constants II ), it wasn't to be seen and known by the people but to exploit them and strip them of the little that was left in the rubble, didn't really fuel the desire to stay with this empire (even the linguistic gap that it got worse and worse it made things worse : knowledge of Greek in the West was in constant decline since the beginning of the fourth century so much so that authors such as Boethius (they wanted to translate the works of Aristotle and Plato into Latin, to make them easier to understand and access)
in fact if the Italians abandoned the Roman Empire over time (even for voluntary abandonment or not by the elite of Constantinople) the idea itself was not forgotten it was only changed to the circumstances it belongs to the Italian priorities (see the choice of the Franks: able to promptly intervene in aid of the pope, speaking the same language or a variant of it not too distant at the time and similar in terms of religious ideas).