As far as I'm concerned, we should make it a goal to work to get safe self driving cars on the road ASAP, and then get really strict on issuing drivers licenses so that almost nobody is allowed to do it.
That goal might be a technically sound one, but I don't think it's politically viable. Telling people they are not allowed to drive their car anymore is likely to be even less popular than telling Americans they can't own a gun anymore.
A more attainable way to improve safety would be to allow people to continue to drive if they want to, but to add intelligent accident-avoidance software to the automobile so that when the person is driving, if the car notices he is about to cause a crash, it can step in and take the necessary actions to avoid or minimize the crash. In this case, if the car noticed that the driver wasn't braking sufficiently to avoid rear-ending the car in front, it could start applying the brakes for him. This approach is not only possible, but is already implemented in some cars.