Anyway Americans pay pretty high taxes, they're comparable to Europe (albeit not as high as crazy countries like Italy, Spain or France, I have no idea how those countries can even survive). I'm sure they'd be more than happy if the government were spending less and letting them to pay less taxes and buy a private insurance instead.
The problem with the US healthcare and higher education is not being private, it's being too expensive - tldr thanks to government intervention some actors got away with massively raising prices with no competition