How could you even compare prices?

If you go in because of a killer stomach ache you could end up needing a CT and emergency surgery. Or you could end up getting some pepto-bismol.

And if you are taken there by an ambulance (which you also have no ability to compare any price to). You'll be sent to the hospital the paramedics decides to drop you off at.

There is an inherent complete lack of information when going in for a medical situation that can't be fixed by the free market. You need (or believe you need) treatment now. There's no way for you to know what that treatment will be.

Even going in for an annual physical can be the exact same. Some dicey numbers on your blood work and you might be looking at some huge unplanned bills that are completely unavoidable.

That's exactly my point.

Number of competitors is only one of the inputs for how competitive a market is, and price intransparency + lack of information on treatment quality make it moot for the healthcare sector in my view.

I don't think higher hospital density would hurt, but we would have to pay for this and I don't see it help drive down prices.