You can then decide if the specialist out of network is worth it, or go in-network or to your medical / medicare provider and work with them.
In particular (for those who don't know) California's law protects you ONLY if you go to an IN NETWORK facility. If you do, then if somehow an out of network doctor drops by or helps with the knock out gas or whatever, they can't then bill you for the "out of network" service. It turns out this was pretty common (my guess is some kind of kickback to the in-network facility to allow this).
You can still be charged or over charged by any provider if you agree to be, and sometimes still even if you don't (ambulance ride to out of network)
"I'm going to buy this great new car. I wonder if it will cost me $15k or $45k? Can't wait to find out!" Said no market participant ever.
A lot of what you said also applies to car mechanics. But they are less regulated, and there's unregulated alternatives, which makes things cheaper and more competitive.
But since the US does have a high amount of government interference (apparently it's a big deal when a child dies, while a dodgy mechanic is something we just deal with), maybe it's best to just create a public system rather than a highly compromised hybrid with most of the cons of both public and private systems (the US actually has a higher tax burden due to healthcare than Canada, since the people who get it free on Medicare and Medicaid end up costing a fortune - the private sector can be way smarter than the government at the subsidies and incentives game).
The free market works great to provide food.
in the US the "free market" for food continually gets porked up "Ag bills", leaves food deserts in low income areas, subsidizes complete and utter garbage used to feed livestock, and pays farmers directly even though it's not efficient by any means.
despite all of this you almost certainly want this to continue because in the event the ol' "free market" decides that it's not worth, say, maintaining food infrastructure due to a few good years, you'll probably die in a famine or the chaos that comes as a result of it.
And just you try to find some competition in terms of food suppliers while you're in a hospital - it's the cafeteria or nothing.
All of these things are untrue of health care.