[dmpk2k]

Yes, the leaders of those nations depend on US influence (and sometimes hard power) to remain in power.

I don’t want to oversimplify things, and yet: how did that come about?

[AYBABTME]

That's a bit of a ridiculously cynical take. The majority of democratic US allies that harbor US bases have a population that supports the presence of the troops. And those in power there aren't so because of the US military power, they were elected.

For dysfunctional or undemocratic nations, it's different.

[reducesuffering]

Poland is the biggest EU supporter of US military presence. You think Andrzej Duda is a patzy of US influence?