With healthcare, we fall into an entirely different domain of economics, especially because the leverage of those who have 'life saving' services over those who don't is basically existential.
A better solution would be: 'one price for everyone'.
The entire gambit of 'negotiated prices' is a fallacy in the end, it's just a matter of groups having collective power over another, it's not really economically efficient.
Either A) all Americans form a 'super powerful buying conglomerate' which is 10x more powerful than any healthcare provider, thereby forcing 'amazingly low prices' (which basically socialized medicine) - or B) we let the 'aggregate market demand' determine price, which is basically 'one price for all'.
America should probably follow one of the European examples where they have a public/private mix. I respect that some people just want full control and want to pay for that, it's fine, but there needs to be a socialized component more efficient than Medicare.
I'm not sure if Canada or UK are the best examples for America. Germany, Netherlands or Switzerland might be better.