Okay, whenever somebody criticizes "the free market" I always have to wonder how much of the market is free, and how much is ruled by legislation. Leonhardt points out in the article that doctors overtreat because of malpractice laws. So ... how free is that market?
And the second thing to consider is that in a free market, by definition, people are getting their money's worth, otherwise they wouldn't enter into the trade. If they enter into trades which can be predicted to be bad, then they need more information. Where's the Medical Consumer Reports? Could it be that liability laws prevent such a thing from existing?
And the third thing is that for the most part, medicine in the US is NOT fee-for-service. In New York State, if you try to buy medical treatment on a fee-for-service basis, the state government imposes a surcharge on you! Most medicine is done like automobile repair. The mechanic (doctor) tells the owner (insurance company) what repairs the car (person) needs, and the owner decides whether it will pay for the repair or not.
Fee-for-service would require a free market in health care, which is something we have too little of, and too much criticism of.