I'm not really sure what your point is, so perhaps I missed something?
Conflating a want for price transparency, so that I can spend rationally where that rationality can be logically exerted doesn't really seem to me a free market ideal as much as it is just common sense. There are many medical decisions made that aren't life or death, and in my admittedly anecdotal experience, that's been most of them. A great many medical demands are inelastic.
When I lopped the (very) tip of my pinky finger off in an accident, it was nowhere near a dire enough injury to worry about the cost of repairs, but it did need stitches. Had there been a repair option, I might have opted for it, but only if the cost was reasonable.
That said, we already know the market value of an ER doctor, or a radiologist; that's how we know what to pay them. It's not as though they're members of some secret cult of faceless men exacting arbitrary payments for their efforts. We know what it takes to pay them, and presumably, they could come up with an hourly cost for their labor plus materials if they so chose. It might take some practice, as estimation is hard, but basically every other service industry in the world is able to do it, so I can't imagine why the medical industry would be exempt.
Regardless, sure, there are plenty of ailments that would hard to estimate, or meaningless to do so, but I don't see why that means nobody should try to do their jobs in a cost effective manner.