Well, I think that in a pure free market, most medical costs would be paid for out-of-pocket. A person would pay the physician and the pharmacist just like the baker. This would keep costs down and reasonable.
To cure a disease or to cure a person who had an accident is of course a lot more expensive and might not be paid for out-of-pocket. Hence, insurance coverage is needed. But notice that you might live a healthy life and the insurance company needs to step in. Insurance payments will be rather rare. Demand and thus prices stay low.
A free market economist would undeniably support a free market in the Health Care Sector. He knows that it works pretty well throughout the economy, why not in Health Care?