The problem is none of these criticisms are most easily solved with "the healthcare system". The healthcare system itself functions quite well.

For instance, almost every bit of infrastructure (virtual or physical) in the US costs twice as much per capita as Europe. That's not something that's wrong with "healthcare". It's not even likely to be a good idea to change that.

Blue states have largely already solved the access issues with subsidies; low income folks do get surprisingly good very cheap access in states like New York and Washington.

Calling out it being "private" isn't even in the top ten things that would improve health outcomes more easily.