It's a bit confusing to figure out who technically owns the bases. https://en.wikipedia.org/wiki/List_of_American_military_installations

As near as I can tell, almost all of them are actually owned by the US. The more important aspect is how it affects the "deal".

The implied "deal" has always been that the US provides military resources to defend "the West" against the USSR/Russia and, in exchange, the US gets to be the primary voice in determining international policy (ie the famous "rules based international order"). That's why the US president has traditionally been referred to as, "the leader of the free world."

That deal has degraded a bit over time as other Western countries recovered from the damage of WWII and started flexing their own power.

Altering the deal so that everyone else pays entirely (or mostly) for its own defense also removes or seriously damages the incentive to follow the US vision of international policy.