"If we focus on a subset of the population that is lucky, we have a great healthcare system." Got it!
Sorry for the sarcasm, but that's how your comment reads.
Do those lucky people have healthcare insurance tied to their employment? Are they afraid to go to a demonstration or advocate a union, because they could lose their job and thus healthcare?
A good healthcare system treats everyone equally, no matter where they live in a country, their income level, being employed/unemployed, etc.
We have a pretty good healthcare system, we just need to subsidize it for people who can't afford it.
No, it is broken. The US healthcare capita costs twice as much per capita as most West European countries and the 'outcomes per capita' are worse. The problem is, similar to the prison system etc., the privatization of the system. It's run by companies that go for profit maximization, which entails rejecting as many claims as possible, driving up medicine prices, etc.
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.