But for things they do cover, what price do they pay? That seems to be the crux here.
Something like travel insurance is simpler, because when they buy you a hotel room / a new suitcase, most of the other buyers are not insurance, and so there's a market price they can refer to. But healthcare isn't like that, and it seems the the prices of many procedures vary wildly, like 100x between different hospitals. Nobody can afford a 100x increase in premiums.
From what I understand about better-functioning health insurance systems, there's usually also a pricelist written up by the government. That seems like the crucial foundation for a useful health insurance market. Much as I wish there was a nice market mechanism for this, I have yet to see one.