Also, insurance does do stuff like that.

They do, I considered adding that, but felt like it detracted from the point.

Any passing glance at the healthcare system immediately reveals that doctors don't give patients cost estimates, inflate costs for insurers, and then settle at negotiated rates. Often they tack on procedures that aren't necessarily part of the initial plan due to unforeseen circumstances while the patient is unconscious and unable to consent, and you can go into a hospital that is ostensibly covered only to find out that a particular provider isn't. It's like if your treads were discovered to be bare, they decided to replace them and then the guy who does wheels sends you his own bill a month later.