To give a more nuanced prospective, I'm an American that has lived in Denmark for 3 years.
Definitely, the American system is a dumpster fire.
Denmark's isn't terrific, either, though. I remember having to call in a favor of my girlfriend's uncle (a doctor) to get a simple doctor appointment that wasn't 4 months out.
Certainly the government does have the people more in mind when making laws - that's not the case in the US. Our government cannot be trusted to have our interests at heart, unfortunately. Pushing for more regulation usually means helping the businesses and not the citizens.
Private health care is cheap and great throughout Europe. You can get an appointment quickly, have doctors that spend time with you, and spend a lot less than you would in the US. The private doctors here in Europe also tend to be better at their job - they've self selected.
The best medical care I've experienced, though, was in south east asia. Most of those countries have a pretty free market. You can even see ads in Bangkok for the price of a baby delivery - front and center on billboards even! Truly a capitalistic health care system.
I've described my own experience with SEA care here:
https://news.ycombinator.com/item?id=15904413
The point is that health care is broken around the world but certain places need different solutions to make it less broken.
America already spends enough public money to afford public health care for everyone but we don't end up with any quality of care for that money.
America is unable to follow Europe on this one even though most european systems would be better.