You confuse “medicine” with health insurance. Free market forces will only regulate the cost of medical care when the financial relationship is between the recipient and the provider. Problems come from the third party, insurers, who come in between. The cost is no longer what I am willing to pay, but what a corporation is willing to pay on my behalf. This raises the cost for all, insured or not.
It is my understanding that a very big element in cost is the mandates of state legislatures. They require that everybody have Cadillac insurance policies when a real insurance market woud allow people to buy policies that meet their needs and priorities. I would never pay what the government is paying for my Medicare HMO, for instance, if it came out of my pocket.
ClaireSolt has it right. We don’t have a free market in health insurance.
I’d get the government completely out of health care, except as court of last resort for contract violations.