The anesthesiologist is in complete control over your life during an operation. If they give you to much anesthesia you're fucked. They must follow all the vital signs, oxygenation etc, and constantly adjust the level of anesthesia given so that you don't slip away.
I'm surprised not more people die, end up in comas or come out with brain damage after operations.
Probably there is a large unknown number of brain damaged people who just don't know it. They probably attribute their problems to something else.