The government regulation catechism is common enough, but that doesn't make it true. And I believe we've already established that we aren't talking about an unfettered free market. I didn't even mention Medicare and Medicaid which are major market distortions.
As long as most of the money goes though insurance, there is little incentive for providers to pay attention to the few demands for pricing information. There are exceptions, of course. Some providers have decided not to accept insurance and either provide fee-for-service or subscription plans. They were put at a serious disadvantage by schemes like the ACA which tried to force everyone into the health insurance pigeon hole.
Trade unions like the AMA are supposed to ensure that their members meet certain standards, so why not let them do that? Or a medical provider can provide credentials which individuals or organizations can verify, and we can base our decisions on that, so some other criteria of our choosing.