That is not the case - as mentioned even in pretty serious cases you might need to wait 1 year or more for something that should be done ASAP, on top of that the quality of the doctors isn't the best. This is especially bad for well-off people (as in middle class) as you pay e.g. 500-1000 USD a month and can't even get a basic check-up.
If you go east and look at Japan[0] which also has socialized healthcare the quality of healthcare there is very good
[0]: https://www.oecd-ilibrary.org/docserver/9789264225817-5-en.p...
You end up with cool things like high trust, and shitty things like intense racism.
Not to mention if it was on the median so bad for citizens you'd see more broad support for repealing it in countries where it is supposedly isn't working, but that isn't really happening either.
Private insurance is not the reason healthcare is expensive in US. The reason is that services and drugs are too expensive because of collusion, lack of sensible regulation and lack of competition.
I paid out of pocket to be able to function. Whatever the solution to American healthcare costs is it's not what we do in EU.