If you were going to die tomorrow ... what would you be willing to pay to live ? 
Everything you have ? And steal a bit on top ? 

Yes, you and everyone else.

And when that is the case - a free market cannot exist, and any market definitely cannot produce either the lowest prices OR the best quality.  Why compete for customers when every customer is desperate enough that no price is too high ? Then raise them insanely and only sell to the rich. That's how you maximise profit.
Of course, globally the law says you CANNOT deny emergency treatment... so now the poor all go to the ER even for sniffles. That makes ER's less effective - and it costs  the rest of us a fortune because ER services are  the most expensive to provide - you really want to preserve them for those who actually need them. 
The most private health country on earth has the worst health outcomes in the developed world, and pays 4 times as much as the ones who save twice as many lives (all the other rich countries).