Based off some of the other comments, here is the idea I’m picking up on:

If a particular market isn’t that competitive and has oligopolistic aspects, more transparency may increase the “effectiveness” of the oligopoly. Instead of hospitals that were charging more lowering prices to compete, we could see hospitals that were charging less raises prices because they know the competitive pressures are weak and they don’t want to leave money on the table.

Seems plausible to me, depending on how oligopolistic most hospital markets are.

The cynic in me thinks this is what you get when you have a very weak correlation between price to outcome, but the perception is that you have a very high correlation between price and outcome. Boards think paying more gets them more, but if it doesn't maybe that just means the price keeps going up as boards attempt to pay more for better outcomes.

I could see something similar happening in healthcare in select locations to some degree, if some hospitals continue to charge more for a specific procedure because the communities they are in are less price conscious and if there's not good information on outcomes to link to the cost. There are plenty of other products out there which cost a premium based on name alone, and there are quite a few very famous hospitals. Usually they are famous for expertise, but that doesn't mean their fame in one area won't lead people to believe they are equally as good or above average in others where they aren't, even if they charge more.

Medical care is not the kind of good that you can just say 'oh the market will correct it', because most of the assumptions you make about 'the market' don't apply to essential services.

Does that apply to labor prices in the given markets, though? We can't force people to work there just because they are essential.