I think only the weakest level of "market-based" can apply here. The government has grossly intervened in the health care market since the WWII wage and price controls implicitly created the business model of employers playing for health care as non-controlled additional compensation, to the explicit post-WWII requirement for emergency rooms to treat everyone who entered.

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."