Self-driving cars can solve "a" problem, just not the one you choose to formulate. Sure, we could probably make things safer by more tightly regulating drivers. But is that desirable? Presumably it is for you, since you likely consider yourself in the group of excellent drivers.
But I wonder if causality actually has any data at all to support his claim. I believe most accidents are less about driving skill and more about experience and attention. And young drivers have less of each. I believe accident data bears this out, as does personal experience.
Human error is very difficult to minimize. Computer error can be made extremely low with proper design, it's really just a matter of how much money we're willing to throw at it.
I actually enjoy driving and have a very good track record and I think well above average "driving skill". Do I think a properly designed self-driving car could be made with a significantly lower accident risk than myself? Absolutely.