Don't kid yourself. It's been peaceful in spite of us injecting ourselves into matters that are none of our concern. We could have achieved the same thing with a few dozen nukes. You don't see anyone lining up to invade North Korea any time soon.
No one is willing to use nukes for smaller wars; so they are off the board.
You need regular military for everything else.
No, you're missing the point. You need a military to defend the homeland. That could be done with a few dozen nukes and the national guard. We do not involve ourselves in 'smaller wars' as we are no longer the world police.