My question is not “Why did Rome fall, but how did they expand and sustain the empire so long? Remarkable for a city to have such an expansive empire for so long.
IIRC the empire was split and they had paid non-Italians for decades to provide an army on the boundaries of the empire. As the barbarians had their own demographic expansion and needed land and wanted a taste of the good life, their southern and western expansions became inevitable. Don’t know how long you can keep your guards at the fence of the property when they want the good life up in the main house.
Rome learned a lot from the Greeks. As a result, it many good policies and practices. This helped it to survive many a bad emperor. Romans also had a very strong sense of honor. Like the Japanese, if you disgraced yourself or your family, you were expected to kill yourself. We can debate the morality of that particular tradition, but methinks it kept their elites on the straight and narrow. [Their mass conversion to Christianity may have weakened this, IMHO]
You also have to remember that the velocity of information back then was very (very) slow compared to today. The reputation of Rome kept her great even after she had rotted internally. Eventually, a few smart barbarians figured out that Rome had become a paper tiger. Even after her fall, it took decades for the word to get out that the Empire was indeed gone for good.