We shouldn't be doing any kind of "banning" here. The question isn't whether or not this would "save lives" because it's not about that. If saving lives was the reason for recommending this kind legislation, then things like smoking cigarettes, guns, and eating in the car would be banned as well. Statistically, eating in the car is the #1 reason for automobile accidents in America. Will they ban drive-thrus? Pretty sure McDonald's would spend billions to make sure that didn't happen. Proposing this kind of ban has only one real benefit: Additional reasons to be stopped by the authorities. In a time when Congress and the WH are going out of their ways to circumvent our civil liberties, any kind of national ban of anything raises my hackles just a bit.
If this was a serious attempt to save lives, there would be a call for legislation increasing the penalties for accidents and reckless driving caused by negligent drivers using their phones. This is something used when driving through work zones on highways. Fines and penalties are doubled.
It's called personal responsibility. Using your phone while driving is a matter of choice and making good decisions.