The US likes having those bases, as they give more ability to project force.
I believe usually the US is not paying significant $ to lease the land that the bases are on.
Also, having the forces 100% under US control and without foreign obligations means that they can come home if the shit really hits the fan.
It is expensive to have a worldwide military force, but, the US has its reasons for making sure its always got its hand in every pie.
Selling our military out as some kind of international guns for hire operation is really not in our best interests.