This, a thousand times this.
It's a SOCIAL problem. It's amazing how many people simply don't get this. You can't engineer away social problems by applying limits. You can only engineer away social problems by changing social behaviors.
Samsung has trialed this approach with great success with S Drive. Rather than try and prevent people from using their phone, encourage people with incentives for using it safely (voice activation only, limits to phone functionality, text to speech interface), and demerit them for unsafe actions (touching the phone while in use). The idea is quite amazing and something like this could be a game changer.
Once you modify behaviors enough that they become instinctive then you can start rolling back the incentives and you have solved the social problem.