It is only emergency rooms where I don't get a choice - if you need an emergency room close is important.
i feel like the folks on here peddling this line have not ever spent any time watching who comes through an ER.
most of the people who go into an ER aren't dying, or screaming in pain. they've just got a problem that can't wait until urgent care opens up again in the morning. or they need something done that urgent cares aren't equipped to do (fancier diagnostic equipment; whatever). they've got plenty of time to consult with a hypothetical "find a cheap/good ER near me" app.
Though I will note that many emergency symptoms turn out to be non-emergency only after more tests.
But as I understand how medical billing actually works, if only a single patient uses an MRI machine in a year, they would pass on the entirety of the cost to the single patient. But a hospital that uses the MRI constantly spreads the cost across all patients. In the latter hospital, they would also have better outcomes since they have more experience and specialization in the procedure.
This is also the opposite of how it would work in a market-based industry. In an auto-shop, I know how much I can charge for any service, and before buying equipment and personnel to expand my services, I determine if it is worthwhile to invest the capital.
That will make surgeons avoid complicated cases due to the risk of failure and its consequences for their careers.
Recently, HSAs and transparent prices were proposed by a Marketwatch article on HN.
But, assuming you have a average America "Max Out Of Pocket", price transparency over this amount doesn't have the intended effect or perhaps, as you point out, the opposite effect.