a sick person looking for treatment is the opposite of everything that makes a market efficient, there's no perfect information, non-coercion etc.
if people want to say, I'd rather people be sick and die and have the freedom to not pay for universal insurance or get vaccinated, that's a values choice. but it's a serious error to say that the free market will result in optimal health outcomes.
I for one am willing to admit that I'm not smart enough to construct a path to a "free market" (a phrase I've never used in this discussion till this message) system after three quarters of a century of massive government intervention.
Heck, it would require an end to "democracy", and/or a few generations of radically changed public schooling, and/or "reeducation" camps for starters. Enough of the people want "socialism", and right now we're seeing the wisdom of Menken's "Democracy is the theory that the common people know what they want, and deserve to get it good and hard.", after the Left has captured just about every institution that matters. The very idea of free market anything in the current environment is ludicrous.
Now Medicare shifts quite a bit of additional costs onto others, you need federal government approval for every new hospital bed, I remember reading some time ago that one state's hospitals were screwed because the state and the federal government had incompatible requirements for hot water temperature, etc. The FDA has massive and politicized control over many system inputs such as drugs and devices, the government has failed to intervene when almost every other country insisted companies sell drugs at near cost (our market supports way more than half the cost of new drug development), etc. etc. etc.
And just before Obamacare was passed the government (mostly Federal with states "partnering" Medicaid) was paying for almost half the nation's healthcare.
A market that was thoroughly intertwingled with governments doesn't really seem up to allowing statements like "It just hasn't worked for health care."