In this market, neither the producer nor the consumer are responding to price signals and often neither knows what anything costs. The Payer (literal healthcare industry terminology) does but isn't producing nor consuming the service.

This is why this isn't a free market. It's not about regulation, it's about the system being divorced from responding to market dynamics.

There are degrees of freedom, but within the American framework, medical care is on the less-free end of the spectrum.

Aside all the insurance stuff, you cannot open an MRI imaging lab or similar without a letter of need from the local government. The supply side is quite literally gated by existing players in the market (via campaign bribes and similar).