At least part of the reason for this is that the West was, for most of history, inferior to China in terms of agricultural productivity, communication over long distances, and centralized state power. So China was always able to maintain more standing forces and stretch wars out over long periods of time, while Western states were generally slaves to the idea of "campaigning seasons" which really only leaves room for one decisive battle. Western kingdoms and empires simply couldn't keep troops in the field like China could. I think that's why wars in Chinese history tended to be much more long, drawn out affairs (like the Han-Chu contention had what 15 battles? Most Roman civil wars had one decisive fight).
The main reason for Qin to maintain such a huge force unlike Western counterpart is exactly because of its policy on conscription. In peacetime, a huge part of the Qin army are actually farmers... however they pick up arms to fight during wartime.
Plus most of the Chinese war actually happened inside China itself... so it is easier to get food in their own turf as they fight.
It was not really true that the western state couldn't keep troops in battle for a long time... I think Richard the Lionheart actually wage a campaign that spanned over years... maybe a decade (I think) and in foreign land.