Even a good you're compelled to buy can be obtained through a free market. Cars are the perfect example because contrary to your understanding, they are actually a basic requirement for a huge number of people. In addition, the vast majority of healthcare expenditures are not emergency, and aren't complicated so there's no reason why people can't obtain a diagnosis from one place and then seek out the best place to actually receive the treatment.

> ...then seek out the best place to actually receive the treatment.

How do they seek out the "best place" if they don't have complete information on what it will cost? It would be like buying cars with no price-tags or MRSPs - yes, there will be good/prestigious dealerships with excellent staff who can tell you the technical details about the car that's right for you, but you won't know how much it will cost you until each component manufacturer sends you their separate itemized bills for months after taking possession of the car, and you can't take the car back (5x tires, 2x wipers, 1x engine, dealership charges, factory charges, line-assembly person 30 minutes @union rates, 1x battery, 348x bolts,1x suspension platform, transmission, etc). That is not a free market.

The problem lies in executing that "seek out the best place to actually receive the treatment". Its hard when healthcare givers do not give a quote or outright misleads. Readers who are not familiar with the American way might find that hard to believe.

In the real world you can't usually separate diagnosis from treatment. The initial diagnosis may change depending on how the patient responds. And it's not always feasible to communicate the important nuances of a particular diagnosis from one doctor to another. Bungled transitions in care are one of the leading causes of harmful medical errors. Care continuity is important for patient safety.

How does the free market account for the cost of researching options?

I am sure I could find a better deal on many medical purchases, but the cost to find them is significant. Purchasing the default/readily-available option is often the best bet because of the hours or days required to find a better solution. Spending a few hours to save $100 or a few days to save $1000 is a clear loss to me.

Most products are extremely complicated. Food and its effects are extraordinarily complicated, but general knowledge about what foods to eat to stay healthy diffuses through an emergent and bottom-up process, through channels like Wikipedia and word-of-mouth.

Cars are another extremely complicated product. Society has self-organized to create reputable sources of information on the quality of different models.

We don't need government restrictions and monopolization of spending to manage the complexity of the economy. Healthcare faces severe problems because of governemnt intervention, not despite of it.