Our way of war emphasizes high technology for mobility, firepower, and the whole C3I thing--command, control, communications, and intelligence.
Consequently, we have a very small tooth-to-tail ratio. American mothers don't want their sons to be armed with nothing better than what the enemy has, fighting on his terrain, where everyone speaks his language, not ours, and where he thinks he's going to paradise if he straps a bomb to himself and blows a couple dozen of us to bits while he's in the act of surrendering.
We want overmatch. And that's expensive in both research/development/acquisition dollars and in manpower.
And anywhere we could expect to fight involves power projection. That's expensive.
BTW, per
Wikipedia, the Russian armed forces contain 900,000 personnel, plus 2.0 million in reserve.
Per
Wikipedia, the Chinese armed forces contain 2.035 million personnel, plus 500,000 in reserve.
Per
Wikipedia, The U.S. armed forces contain 1.381 million personnel, plus 845,000 in reserve.
Per
Wikipedia, Russia also has 554,000 paramilitary troops, China has 660,000 paramilitary troops, and we have none.
Those three are basically in the same ballpark. But a far greater percentage of hour manpower is involved in projecting power rather than being bayonet-stickers, trigger-pullers, cannon-firers, and bomb-droppers, in comparison to those other two.
If all we had to do was defend our own shores, as was the case in the 19th century, then we could cut our forces in half and feel reasonably confidant that we could defeat an invader. Maybe not strong enough to deter an invasion, but probably strong enough to defeat one. If we didn't just decide to surrender when the ships showed up on our shores and bombs started dropping on our cities.