I would worry that a fair market value for healthcare would still be more than most people could afford. The question is, would it be less out of pocket or more than with insurance, which is probably a vague question and one I have no ability to attempt answering. Anecdotally, though, I've found that while the squeeze of my employer's health plan was difficult, having to pay the entire cost of my appendectomy would've been nigh impossible. I can only imagine how much my mother with COPD would have to pay out of pocket.
Everyone thinks that the market value of something will be more than they can afford. So they implement policies that are guaranteed to make the price higher.
Every commodity costs something. The best way to distribute a limited number of goods to a maximum number of people is a free market with a free price system. There will always be the poor who require charity to be taken care of. There will always be the rich who can afford the million-dollar life-saving procedure (but of course in time that procedure will get cheaper).