This would all be well and good if the doctors weren't also profiteering. When you visit one, you still don't know if their recommendations are good for me or for them. I have seen allergists which are no less slimy than used car salesmen. See also studies on dentists and their varied recommendations for the same patient.
The US insurance system doesn't seem to be giving us low prices, but let's not pretend it's all their fault. It's just a complex market where it's hard to compare providers, and therefore is prone to a lot of inefficiency.