You don't even need self-driving cars to do it, and it would greatly reduce the number of serious accidents and fatalities. You could start with just the roads with the most accidents.
And by the way, nobody seems to have mentioned that assisted driving technology could be added to cars today. We already have cars that emergency-brake for us. They could also warn us of upcoming red lights, fast approaching obstructions in the roadway, or unsafe actions on the road, such as letting the car drift lanes without a turn signal.