Late Stage Capitalism

There was some private industry and profit, but at the end of the day, it was all about enriching the empire and giving the people bread and circuses to keep them quiet.

Less than you might think! The Imperial state apparatus was actually very skeletal compared to what we think of it, at least during the height of the Empire. We're talking entire provinces with only a few dozen actual imperial officials to manage it, most of whom brought their own private staffs. Senators were formally barred from large-scale commerce, but they got around this by investing their money with non-office-holding individuals to engage in business on an obscene scale. Most of the resources moving around were moved by private trade, and at immense profit. Only a few resources were subject to imperial monopolies or had widespread imperial control; everyone else was playing a more-or-less recognizable hustle of commerce - buy or lease cheap, produce at low cost, sell at high profit.

Every Roman citizen got fed. Which is pretty anti-capitalistic.

Not even close, I'm afraid! Even in the city of Rome itself, and it was only in the city itself where the grain dole was in effect, it was limited to a certain number of citizens, and most of it was sold subsidized by the state rather than free. Those citizens who received the grain dole, furthermore, were not selected out of the poorest of the poor - it was largely the established working families - semiskilled workers, artisans. small merchants and the like, who might be expected to have times of hardship but not be in constant danger of starvation - it was a political subsidy to these people, who still had some social pull and connections in the city but were not integrated enough into the power structures to have a firm interest in sustaining it, to keep them from calling for anything dangerous, like more democracy!

The ultra-impoverished largely were left to the issue of charity and political patronage (which was big in Rome), and starved about as much as any impoverished pre-modern group. Maybe a little less, considering votes were almost literally bought long after voting ceased to be meaningful. One supposes that's a bit more money than most would have.