My wife is from mexico, so while her visiting familly there I've had some opportunity to interact with and observe their system.
It seems better!
There are public hospitals which are open to all. The quality and wait times are reasonble, not fantastic. There is very little paperwork. (You don't have to jump through hoops like signing up for Medicaid or something.)
Alongside that, you can buy private insurance and go to private hospitals, which, in my (admittedly limited) experience, are very good -- efficient and reasonably priced. I would _guess_ because of less regulation and because they have to provide value above and beyond the free healthcare that's available?
In the US we seem to have created sort of the opposite incentive structure -- public healthcare is only available to a limited set of people, and everyone else is more or less forced into the private healthcare system (or "private", since it seems heavily intertwined w/ govt -- e.g., standard govt websites to pick a povider, tax penalty (tho since lifted) if you aren't signed up).
Somehow there's always a mountain of paperwork and bills that dribble in over months, and you never know how much the final cost is going to be.
Another seemingly-insane feature of the US system is if I pay for a service w/o insurance, I'll be billed some crazy rate. With insurance, I'll copay some reasonable-ish rate, and the insurance company will also pay some reasonable rate, often at like a 90% discount to the "quoted" rate. It feels like I'm coerced into insurance because I can't out-of-pocket pay the actual real reasonable rates.
Another annoyance is it also doesn't seem possible to buy insurance that just covers accidents, which I would personally do if I could...