It's true the free market isn't functioning in healthcare. You mentioned doctor supply. During the late 1990s the American Medical Association convinced the government there was going to be a "doctor glut" so the American taxpayer subsidized medical schools in exchange for not graduating doctors, $100,000 for each doctor not trained.
You give a good example but it is worth clarifying that more than it being a non-functioning free market, it is absolutely not even close to being a free market. The Federal government is the biggest spender in the market, and with that comes a mountain of regulation and price controls. The states are probably the second biggest players in the market. Even things that almost everyone would agree with make it a less free market, like licensing doctors, certifying medical schools, and approving drugs. I think you could make the case that either a much freer market, or a completely state controlled system would lead to lower costs. The current situation reminds me of the pseudo deregulation of power in California that ended in catastrophe.
