That's not true. Poor people can get Medicaid, old people can get Medicare, and there are also various other ways of getting one's health care expenses subsidized by the government if you're poor or have medical reasons for not being able to work.

Just to be clear:

I'm for 100% state-funded medical care, but it's simply not true that "the government doesn't pay for anything; only private insurers do". The government does pay for quite a lot, even if many people in the US don't qualify for such aid.

They absolutely should qualify for such aid, in my view, but my opinion doesn't change anything. Some people qualify, some don't, and the government does pay for some, and private insurance does not pay for absolutely everything in the US. These are just facts.