You mean have someone check before surgery that patients probably won't have anything unusual happen, (not standing in the operating room going "let's not do the surgery, there was a misdiagnosis", which would cost even more)? That's bad for patients who do look unexpected inside, and cases where the surgeon messes up in a way that didn't come up during training. The cost may well still be lower than that of doctor training that rarely gets used.

There are specialized phlebotomists who do their job perfectly, and that's probably feasible (maybe actually implemented?) for much minor surgery.