It would be interesting to see if painting lurid stripes on the car as a punishment would help. Or require the driver to have warning sign attached in prominent places. Make it as embarrassing as possible.
Can we do this for other driving offenses? Like drivers who don't signal lane changes or drive slowly in the passing lane? I'm all about publicly shaming drivers into doing better.
People drive with suspended licenses all the time. What I'd really like to see upon conviction for distracted driving or drunk driving (similarly dangerous) is criminal forfeiture of the offender's vehicle and a court order prohibiting the offender from owning or possessing an automobile.
Make a phone-themed one!