>>17988790 (OP)
It was. Was it better than Rome in 10 AD? No. But it was a heck of a lot better than the chaos that ruled in the West during Ricimers dictatorship and in the interregnum after his death. Odoacer's dissolution of the Western Emperorship was necessary at that point. We have all these maps but they do not reflect of the Empire actually looked in say 450 and 550 in the minds of the people. Rome having fallen is relative, since Rome wasn't the capital anymore anyways. No one in 476 thought Rome had fallen, not until Justinian's propaganda convinced the Eastern citizens of this fact which lead to the reconquest.
When did Rome stop being the most important city in the Empire? 330 when Constatine founded New Rome? 402 when Ravenna became the capital? Maybe even 313 when Mediolanum became the capital? By 700 it was no longer the most populous city in Italy. Rome fell before the Roman Empire, but by the 800s Eastern Rome had certainly become Byzantium and scarcely resembled even late Roman institutions.
The city may have fallen. New Rome may have fallen. But the Roman Empire? It dissolved until people no longer thought of the Roman Empire as existing but as passed and past. The empire was simply so universal, so expansive, so long lasting in its multifarious iterations that Rome became the basis through which barbarian kingdoms experienced the western world as a whole. Where the Romans thought in frontiers and hellenism in the east, where they lived in a world shaped still by the ancients. The basis for european civilization budded in the seedbed that were Roman ruins.