The market, alone, doesn't work for medicine, because citizens' needs exceed the capital that they have available to finance the labor to meet those needs. If you want a free market to solve medicine, you must accept individuals being denied care. It must be made an excludable good. I, and to my knowledge most US citizens, don't believe that healthcare, at least basic care (yearly doctor's visits, diabetes management, childbirth, etc.), should be excludable. Indeed, most of us, including myself, would be unhappy for someone with a gunshot wound to be turned away. As soon as we make healthcare all inclusive, we need something more complicated than "the almighty invisible hand".