I posted an interview about the open-pricing surgery center of Oklahoma which actually goes into how a free market healthcare system would work.

A free market system would make for even more uneven differentiation in health care quality - with some people not being able to receive care at all at the end of the day. Yes, on average we would have better health outcomes (same as most people would have better outcomes on average if you didn't require car insurance, since most people don't end up using it), but the few outlier cases would be significantly more tragic than they already are.