To be fair, I come from a country where we have free healthcare, free education up to college level (we only pay when taking masters or things like that, after finishing our chosen career. Our most know public university is pretty top notch if we talk about content and education quality. And our healthcare is pretty good too, although there is also private healthcare and education. In the education department, at least to my knowledge, there is not really a difference. The USA is not big. It spends a lot on defense (which usually use to wage innecesary wars or disrupt other governments) and maybe too much in mantaining this horrible two party system you've got. That said, my country's economy is in very bad shape (Argentina has inflation rates that are sky high).

Why on earth would we want the government funding and running things

I'll take competency issues over greed and harm anytime.