Non-Americans, yes, but Americans pay taxes to use it. In fact, if you replaced tax-funded model with, say, a markup on each receiver, Americans would pay less than they already do, and only those that use it would pay for it. I find both of these things beneficial.
> Had the US not provided for civilian access to GPS, and instead there were several competing private systems, they would all be worse
Why, though? Why would they be worse? Typically, when you have even two competitors, the quality is improved.
> and every application which is today based on GPS would have an additional monthly fee to access whichever private constellation that application had built around.
You are lacking imagination. It’s like saying that if government stops providing internet connectivity for free, every application accessing the internet will charge monthly fee. Alas, government does not provide free internet, but nevertheless, apps don’t charge consumers for ingress/egress.
As it happens, businesses are pretty good at coming up with business models convenient to users. Google could, for example, easily cover the entire cost of GPS completely on its own, and offer free Google Maps, which would easily outcompete other map apps if they charged money for use. Considering how much they pay for being default search engine on Apple, $1B is a pittance.