I don't believe a computer will ever be as good a driver as I am in my lifetime in terms of my personal safety, except for when I'm really old and possibly can't see well.
The vast majority of accidents by human drivers are caused by basic neglect, not tricky edge case situations. I think it's hard to really comprehend just how bad humans are at driving. It wouldn't take anything close to a perfect autonomous system to do better--just having "drivers" that actually pay attention to their surroundings all the time would be a massive improvement, even if there were occasional bugs and glitches.
Really? No one knows if we will ever improve on self-driving cars than the current technology today? I'm going to stick my neck out and say "Yes, I know that will move past that."