Motives for American Empire

What are our political leaders’ motivations in stationing so many troops in Germany, Japan, and South Korea? How about the empire in general?

I see two clear motives - defense contracting and dollar hegemony. I suppose stationing troops contributes to contracting. Does it contribute to dollar hegemony?

Older empires grew to expand tax horizons. Are we doing this by means of the dollar? For example, the Iraq invasion occurred not long after Saddam switched oil sales to the Euro. It seems keeping middle eastern oil on the dollar is a means of extracting wealth from the world.

Are there other ways American empire does such?

The motive of power is power.

So long as they’re not paying for the empire, they like to have it.

They’re both this. But in regards to this it’s important to note that most countries “occupied” by America, at least in Europe, want them there. It’s pretty much a quid pro quo for the dollar hegemony.