Well you are again using primary sources on their own. Why are the sources to be trusted on their own to begin with? @John7755 يوحنا mentioned Sassanids and Abbassids, but I'd mention also the Byzantines, where did all those men go after late Antiquity? Are we to actually believe that peninsular Greece alone had the ability to provide for about as many or even more men than the Byzantine empire between the 7th and 12th century? Because that's consequence of the assumptions you make.
As other people have pointed out, there's no reason to suppose that all states throughout history could only mobilise the same proportion of their citizenry. And as for the Byzantines specifically, 7th-century Byzantium had gone through a lot of wars (against the Sassanids, Arab invasion, Slavic invasion, Lombard invasion...), which presumably would have depleted their manpower reserves quite a bit.
The Italian army in 1866 was even smaller than this supposed 250k figure, when Italy had 3-4 times the population of Roman Italy at that time. Mobilizing 5% of your population(meaning a lot of your working age male population), amassing 40% of them for one engagements is an extremely arduous task for any nation.
The Italian army in 1866 was a professional army, not a militia. And the Roman Republic was, like all pre-modern states, very rural by modern standards. Farming is one of those jobs which is very labour-intensive at certain times of the year (specifically sowing and harvesting, when you want to get everybody available to work), and much less so at other times. Yes you still need to weed the crops and so on, but you can generally afford to send a member of your family off to kill Gauls for a few weeks without much of an impact. Conversely, when you're working in a factory, production tends to be much more constant throughout the year, so having a significant portion of your workforce go off to join the army is going to affect business in a way that wouldn't happen on a farm.
The Romans spent plenty on public works, specifically in the imperial era they also had subsidies of various kinds, internal and external. Even the professional Roman army of the late principate didn't compromise all of the state expenditure(it amounted to about 60-65%) and left a lot of room for other stuff.
Public works were mostly one-offs funded with the spoils of successful campaigns, not regular expenditures. And third-century BC Republican Rome generally had fewer subsidies than Imperial Rome.
Achaemenid statistics do not work either. If we assume 49 million population at their height, an army of 2 million would comprise 4% of the total empire. Is anyone of the opinion that a massive polyglot empire, ruled by a minority of Elamo-Persians who experience frequent satrap revolts, is able to conscript 4% of their entire population? If I am not mistaken either, this would be that 2% of the world (which I do not buy that the empire possessed this much percentage of the world population) population was levied to invade Greece alone!
I don't think anybody's been suggesting that the Achaemenids sent two million men to Greece; estimates I've seen tend to be around 150-300k.
Assyria, an empire with greater militarist focus and similar population was only able to levy 90k warriors in a population of some 11 million at least, comprising an estimated .008% of the populace. If your view is that the Elamites-Persians were that superior in conscriptions than the greatest military power of the ancient near east, then there is nothing more to say.
Well, if we look at territories conquered -- not a perfect measure of military prowess, but not a bad one, either -- the Persians seem to come out far above the Assyrians. So I'm not sure that the Assyrians really can be described as the greatest military power.
Even in China, most battles in the 7th century under the Tang have less than 80k soldiers combatting. At Suiyang, the combat over this location lasted a year and the Yan forces sent 100k over an entire year to take the location! In the wars in Korea, the Tang armies are less than 40k always and the Koreans vary and are always below 50k. At Talas, the Anxi protectorate arrived with no more than 25k warriors. Is the opinion of the opposing posters, that Greek city states could levy greater numbers of soldiers than the Tang Dynasty!?
I'm not sure what you're trying to argue here? The Tang undoubtedly had far greater resources than ancient Greece, but they obviously didn't mobilise all of those resources for single battles, so there's nothing strange about the idea that a Greek army in a particular battle or campaign should have been larger than a Tang army in a particular battle or campaign.