Earlier quoted context omitted.
There's no such thing as a "free market" for healthcare. The ability for consumers to exit a market is one of the prerequisites for the invisible hand effect. You can't exit the healthcare market.
You also can't exit the food market, or the shelter market, or the clothing market, yet those seem to work much better.
I challenge you to find the price of a cancer treatment regime protocol in the United States. I will bet you any amount of money you care to wager that no US provider exists anywhere that will give you a price quote for lung cancer treatment in writing anytime before that treatment is provided.
And even IF you could, that only covers the cases where you are still have enough health and mind to rationally evaluate the prices. If you've been in a car accident and are dragged unconscious and bleeding into the ER, you can't shop around, even if they DID give you a price, which they certainly won't until you're already treated.