However in healthcare that's not an option, there is no competition. The cost of fixed cost procedures (e.g. lab work) are unknown. You can't shop around for surgeries or doctors. Everything is wrapping in mystery even after the fact, there is no final bill. Even if you pay everything you're asked to, you might still get a bill 2 years down the road for reasons no one can suitably explain.
The same is not true with healthcare - you may go in for a $20K stent, but have a serious complication that needs $200K open heart surgery -- you don't really have the option to say "put everything back together and I'll live with it".
It's not just an expectation, it's the law in many places. When I was a pro mechanic in Indiana, anything over original estimate + 10%, and authorization from the customer is required. Well, not required I guess, since if you show up and the bill is 20% over, you just pay the original estimate. (Yes, in the worst case you might have to sue to get your car back. Personally, I've never known that to have happened, because most shops aren't looking to rip you off.)
But, as you point out, me being in the middle of a top end job is a little different than a surgeon who's working on a running engine when it comes to needed extra work.
Complications during surgery aren't necessarily caused by the surgeon or known ahead of time. The same is true of other things like home renovation where "we won't know until we open her up" is a common enough phrase.
Case in point, we want to remodel a bathroom that has a 7ft ceiling and my wife wants the ceiling raised to match all of the others. Why is it 7ft instead of 8ft? Can it be raised? Without significant cost? We won't know until we get in there.
I don't think that's the case. For example, if you get a lipid panel, it's going to be coded under a given CPT. The billing department should be able to obtain the cash and insurance price. The problem is that they're not forthcoming with it (at least in my experience even when I had the CPT).
Basic supply and demand theory depends on consumers having perfect information. A free market cannot work when a consumer has no information.