The problem with letting the market decide is that the market is concerned with making a profit, providing "care" is just the means to that end. As long as insurance providers make money by denying care, they will do so, with little or no remorse. The results of this is that we spend more on our health insurance than any other country, yet most of us our still one major illness or accident away from financial ruin. Single payer health insurance is not "socialism," it's compassion and common sense.
Incidentally, one notable policy difference between Hillary and Obama is on this subject, with Hillary's plan closer to the universal coverage we all need. If Obama wins the nomination and hopefully, the White House, Hillary could spearhead a drive towards universal care from the Senate. Her "Hillarycare" was sneered at in the past, but I think the American people, if not the politicians, are ready for it. At least it's about care, not profit and that's whare we need to start.