Why were the ancient armies (Roman, Persians, Greeks, etc.) so much larger than the armies of the 700s-1800s?

They lied. End of story.

At Tigranocerta, the Romans - Appian IIRC- claimed to have 10,000 men, two legions, with which they defeated the Armenian forces numbering upwards of 300,000 with Kataphracts, Heavy Infantry etc etc. 300,000 is actually on the average side of things, apparently the Armenians had 700+K troops according to some commentators.

Yeah, right.

This wasn't the end of it. The Emperor Valens had around 15000 men at Adrianople during his battle with the Goth whatshisname, who'd scrounged up around 10000 fighters from his refugee camp numbering approx 30000 (he did get vital reinforcements later).

BTW- what do “modern skeptical” Firang historians say was the size of the Roman Army of the East in the 4th Century? 500000? 650000?

Yeah, right.

At the end of the day, history is a set of lies agreed upon and, since we are all not islands into ourselves, it means we are all subsconciously acting in aid of some grand end, which only the utmost untermensch would confused with vague meaningless inanities like “Truth”. Case in point being our great TWs on Quora- many of whom have so enthusiastically defended the Bengal Famine in their time that I wouldn't be surprised that they'd been, in a earlier birth, the British Army officers who'd architected it.

Anyway…

Around the turn of the century before the last, Hans Delbruck had covered some of the vital aspects to be considered while reading accounts of such texts. I recommend his works for those interested, but remember certain issues remain.

As for how to gauge a “plausible” size of armies, it's complicated and relies a lot on subjective aspects but there are ways. I'll give an example.

Chodaganga Orissa, around the 13th Century, maintained a standing force of roughly 45K-47K troops, mailed and equipped, with roughly 1 man for every 100 vatis of land. Merely maintaining this force took up around a third of the total Chodaganga budget of around 1.5–1.6 crore madhas.

However this didn't mean Chodaganga generals actually fielded this force in battles. Bar a few situations, the typical Oriya army would've most likely numbered around 10K-12K. It'd need almost 600 vehicles to transport its requirements, a vast column strung out over 5 kms. The average 14th Century Oriya force could cover 35 kms a day but this was dependent on multiple factors- including the solvency of the State. Two months of campaigning with a 15K force would force Gajapatis to start borrowing, the full army would exhaust the treasury even sooner. Entire wagon loads would be eaten. Like Sarala Das once joked, such an army would drink streams and piss out ponds.

Personally, I'm really skeptical ANY Indian State could field a force of more than 150K at a time. I see no reason to suspect it was different for the rest of the World. It's literally impossible. Chevauchee and “living off the Earth” could manage higher numbers- but let's recall the rule of thumb: for every extra Anikini, it'd have devastated an equivalent amount of land during the march. So it's going to be murders, rapes, desertions, and a massive moving famine. Charming.

Anyway, we know that the old Mediterranean Empires in Rome and Greece appear to subsisting more upon whatever pop culture BS Quora TWs seem to pick up rather than anything seemingly based on truth, so it's immaterial TBH.