[tropo]

Private healthcare providers in the USA are not like that. The hospitals are normally glad to accept your money in exchange for treatment. You can go elsewhere if you wish. If your insurance company denies payment, you can find some other way to pay.

Canada prohibits the existence of private healthcare providers. The only reason people aren't condemned to die on waiting lists is that nearly all Canadians can easily travel to the USA when they are desperate for treatment. Canada saves money because people are using their own funds to purchase treatment in the USA.

The UK will actually prohibit people from seeking care in other countries. I guess it would be an embarrassment if you got care elsewhere, so instead you must die.

There, that's two developed countries. I don't wish to research every damn country in the world, and you said "free to pick any developed country to compare to - it won't matter". I picked them because they are English-speaking and relatively large.

I'm not interested in generic "better outcomes and lower expenditures". That just means that everybody gets substandard ("cost effective") care. I want to live in a country where a person over the age of 80 can get an expensive treatment to improve quality of life. I know a person who did: first about $80,000 in drugs for hepatitis, then a hip replacement. Neither would happen in a country with socialized healthcare because she wouldn't be worth the money. They'd estimate something like "quality adjusted years of life", determine the value is low, and give her some pain pills.