---why are American forces in these nations?---
Because it's better to fight over there than over here. It's forward defence.
I tell the kids I work with to imagine having to defend your family during a gang fight. I ask them if they'd rather do it in their own front yard, or a couple of blocks away, in someone else's front yard.
There is always collateral damage in war. Since that is true, I'd much rather someone else suffer the casualties than us. So would most of our soldiers, sailors, airmen, marines, and coasties.