alt Hacker News> Rome was able to field huge armies by the 3rd century BC already, originally sourced from the Italian peninsula alone.
That's true, but the contrast to other contemporary states is not felt to be one of population size. Rather, the Romans were able to mobilize a much larger share of their subject population into the army.
This would be an interesting debate, but it is after midnight here, so I will be going to sleep shortly.
Basically, yes, but also no. There is a huge difference between being able to mobilize a large portion of your population for a short time vs. keeping the standing army indefinitely. With the latter, various intrinsic economic limitations will bite. Rome started with the "big temporary armies" model, but slowly transitioned into "big permanent armies" model, which required a lot of support from civilians.
Professional soldiers are economically unproductive; they have to be fed, clothed and provided with weapons. Just the necessary smelting of iron in order to equip a single legion would be a lot of work for blacksmiths, miners and lumberjacks who produced the necessary wood for charcoal. If a premodern empire can field tens of thousands of iron-clad professional soldiers indefinitely, it must have a lot of civilian workers supporting that army. Literally millions.
The precipitous drop in the size of field armies in the Early Middle Ages is a good indication of the precipitous drop of the entire economy which would prop them up.