You forgot the main reason - volatility between our allies and their potential enemies. Peace is a like spider thread holding the world together. At any given moment, a war could break out. Granted that we have tons of nuclear weapons at our disposal but using them is a last resort. I believe the U.S. would be the last one to use them unless we had no other choice.
Look at the world today. While there are no active major wars going on, that doesn't mean everything is hunky dory. Japan and China are clashing over the South China Sea. Argentina and Britain keep thumping their chests at each other over the Falklands. Iran has threatened numerous times to shut down the Strait of Hormuz. All of these things will impact us whether some believe that or not.
Now I realize that a lot of people in the U.S. are tired of us sending troops overseas and getting stuck in a peacekeeping/rebuilding effort and I am one of them also. But if our allies find themselves in a bad situation, where their potential survival is at risk and they couldn't handle alone, it would be a clear sign of abandonment if we told them we wouldn't help them. One day we may need their help. Having a substantial standing army means we can help them without putting our own security at major risk.