Healthcare in the US is definitely not driven by the free market. It is probably one of the most regulated industries. Whatever disfunction you want to call out in US healthcare it is going to be difficult to pin that on the free market.
You're conflating 'capitalism' with 'free market'. You can have either without the other and OP was calling out 'capitalism' specifically.
Of course the US market is highly regulated and so the market is not free to lower prices. Of course the AMA is a racket. Of course needs of certificate are abhorrent.
Given the customer non—coerced access to his preferred provider, and not taking his money and slapping a bunch of regulations on him will of course lower prices and give him better care.
I don’t see why the other side can’t see it.