As a quick aside, cops in general seem to be pretty shitty drivers. Had a couple incidents where cops who were simply talking to their partners nearly swerved in to me.
But, more to the point, it's a slippery slope issue. Eating in your car is also distracting. Do you solve it by banning drive-throughs? Reading in your car is a distraction. Do cops issue tickets if they see an atlas or a copy of the local newspaper on the seat when they pull you over? How about if you jotted down directions to where you're going, and a cop sees you check the paper to see if your exit is coming up? How about unruly kids in the back seat? Quite distracting, but you don't hear calls for kids to be anesthetized before getting in a car (although...).
Point is, if the government takes it upon themselves to enact a new rule, regulation, or prohibition for every danger in the world, then there's nothing you can do freely. There are laws against swerving dangerously from lane to lane in traffic. There are laws against running people over, or slamming blindly headlong into a telephone poll. Some people can multitask to the point where they can talk on the phone and drive. Some people need a hands-free device to achieve the same result. Some people (and I'm in this category) would rather stammer through a conversation and lose their train of thought because their primary focus is on driving, not talking. Some people just can't pull it off at all. You, like most statists, are proposing a one-size-fits-all solution to a problem that doesn't have one. At its core, what you suggest is no different than solving alcoholism or other forms of drug abuse through prohibition.