General anestesia is pretty secure, but 1:100.000 still end deadly. Thats why general anesthesia is avoided whenever possible, especially for small procedures like that. It’s also way more complicated, requiring a pre-medication talk, an anesthetist being present and supervised rooms where patients can wake up.

I've wondered quite a lot about this. Look, the last thing you want to hear while the procedure is being performed is the surgeon saying: "Please, stop moving your eye. Help me out here".