Perhaps it doesn't, for those weird edge cases where they have to bring the unconscious patient in and have him assessed 5 different ways. Situations like that are the domain of insurance agencies.

But most medical care (the majority of the cost) is not rendered like that. Most of it is routine and predictable, and should be priced transparently as such.

Not a necessarily a supporter of free markets, but I’d argue that more information and transparency is crucial for market efficiency. Take for example arbitrage; it disappears when enough people have access to “private information”, that in game theoretic setting, drive market price to equal the “true” price.