You're probably right, at least they would have for awhile. But these kinds of sacrifices are not necessary. We have the ability to wipe out entire countries without the massive use of resources, or soldiers for that matter. It is this ridiculous idea of nation building that is putting a strain on us, not the actual war itself.
But even if you wipe a country off the map, you still need "boots on the ground" to occupy the land. It doesn't matter whether you opt for nation building or ruling the conquered land as a colony, you still need infantry to occupy and control.
Most importantly, you need a nation to back your mission and your soldiers. Even without shared sacrifice, a nation needs to speak with one voice and one mighty resolve. Compare our resolve in World War II (and the means that the government used to achieve it) with our resolve in this war, and you'll see what I'm getting at.