One difference with auto repair: I expect the garage to call me before they do any work that exceeds the estimate. And I may very well decide not to do it. They may tell me that I need a $1000 timing belt replacement when I ask for a $200 water pump replacement, and I may decide not to do it. I can even ask them to put everything back together and tow the car somewhere else for repairs. If they tell me I need a $3000 engine replacement, I may decide to just scrap the car.
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".
One difference with auto repair: I expect the garage to call me before they do any work that exceeds the estimate.
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.
I've often thought this could be solved by requiring a doctor to carry "estimate" insurance. The patient's bill would be the quoted price and the doctor's insurance would cover any complications leading to additional costs. This would have the additional benefit of increasing the costs of doctors with frequent complications. This would only work for immediate complications from surgery (i.e., less likely to be impacted by patient compliance).
It might also lead to doctors "missing" complications to avoid insurance premium increases.
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.
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".