As to the earlier question about Theodoric's cultural and physical resources, I'd like to go a little further back in history. Rome, as the center of a pan-Mediterranean Empire 2000 years ago, doesn't make a whole lot of sense, especially when compared with, say, Carthage, Alexandria, Antioch or even Massillia. Rome really produced only one product in surplus: law. The trade ships which traversed the Mediterranean weren't bringing Roman products out to the provinces; they were bringing the surplus of the Empire to Rome to be consumed by the wealthy, and shipping supplies out to the legions on the periphery, to keep Rome in power. Local chieftains during the expansion and consolidation of the Empire were bought off, brought to Rome and Romanized, and their peasantry became, accordingly, Roman peasants. Along the frontiers, individual barbarians and small tribal units, really more extended clans than anything else, would acquire a taste for Roman living: the baths, the wine, the games, and all that came with becoming first a villager and then a city dweller. The chieftains would be wealthy enough to live in true Roman style, and perhaps to live in the City itself, or at least one of the mini-Romes, like Trier, Cologne, or Belgrade, planted on the frontier as a way of paying off old legionaries. Poorer tribe members would join the legions themselves, indeed would eventually more or less become the legions, and hope that at the end of their 20 year stint, they'd get their forty acres and a public bath. They wanted to become Roman, in other words. And the genius of Rome while it was still the capital of the empire is that it let them.
However, when the true seat of power, or at least administration, moved to Byzantium, that changed the dynamics and economy of the Italian peninsula. No longer was Rome the stomach of the empire; that happy position passed to Constantinople. Over the fourth century, it doesn't seem to have mattered all that much. The entire empire was enjoying the boom that came with the stability that Diocletian and especially Constantine provided in contrast to the tumultuous third century, and, as the Renaissance demonstrated, a gigantic plague like the plague of Cyprian may have many devastating effects, but it also tends to be a marvellous redistributor of wealth. So, the Italian peninsula in the fourth century was probably able to putter on for a while off of the capital assembled during the long reign of Rome (the city). However, a century of being more or less a backwater will have its economic effects (look what 30 years of being a backwater has done to Detroit). Italy, by the fifth century, was accustomed to looking backwards, not forward.
Now, if you're an emperor, are you going to prioritize defending a backwater? Not bloody likely. When the competition for a defense dollar comes down to spending a little extra bit on keeping the Persians out of the richest area of your realm, the Levant and Egypt, or keeping some barbarian tribe out of a province you've barely ever heard of on the upper Danube or lower Rhine, several mountain ranges away from where you're at, it's not really hard to decide where your attention will be focused. Thus, it becomes much easier for barbarians to move in in the west versus the east. These barbarians want to stay. They want to defend their new homelands. They want to pay taxes and tribute. Excellent! They want a say of what goes on in their new homelands, though, too. Bogus.
Sometimes, emperors would bite on that deal, sometimes they wouldn't. Unfortunately for the western empire, one of the tribes that they didn't really adopt as foederati was the Vandals, and the Vandals had a cool idea: Africa looks fat and unguarded, why don't we go there? In my opinion, Vandal Africa was the mortal blow that killed an Italian-centered western empire. The Vandals continued trading African grain with the rest of the empire, but on significantly different terms than Africa's trade before the Vandals. No longer was the African surplus creamed off to purchase luxuries in Rome, or at least to keep the poor fed in Rome. No, now it was being used to bring luxuries to Africa. Plus, like the Vikings and English would later demonstrate, the difference between trader and raider often comes down to whether or not you have more killpower than the people you encounter on the sealanes. So, the bottom dropped out of the traditional imperial economy in the Italian peninsula.