Waking up during surgery is definitely a complication. And individuals rarely decide to sue everyone. It's the lawyer who sues anyone involved, in the expectation that at least one of them will stick.
Personally, never having been in this position, I can only answer hypothetically, but I am aware that, due to variations in body chemistry, some anesthesia medications may not work as well on some people. I would certainly want to know why I woke up, if for no other reason than to make sure it couldn't happen again. But unless I was fairly sure of negligence I wouldn't feel right suing anyone. I don't feel that a lawsuit should be a quick way to a small fortune, especially in circumstances where no one did anything wrong.