I totaled two cars that way one wet night - mine, and that of the idiot college-freshman-to-be who made an illegal left into the intersection a couple hundred feet in front of me, because of the kitten wandering around the cabin. (The kitten came through just fine.)
No it SHOULDn'T be illegal. You know whats wrong with the world? People naturally have freedoms in this world, and its only by giving them away subtractively that we are losing ourselves. Pretty soon you will vote to make it illegal to bite your nails because it might hurt you. I can hear you saying now "YEAH I AGREE WITH THAT BECAUSE PEOPLE GET HURT AND THIS WILL HELP THEM AGAINST THEIR WILL." Screw that attitude. I have a small dog and he is just fine and polite in the car. I can't put a seat belt on him but its abuse to have him in the apartment by himself so we go riding. And I don't tie him up. He isn't a danger. I could be in more DANGER from being careless and irresponsible with my driving and attention.
Its the same thing with gun laws. Stupid people kill people. Not the guns. You are taking away "guns" and emboldening people who already don't follow the law. Your idea to make a LAW to make it illegal to have an unrestrained dog in the vehicle is ineffective and naive. It doesn't do a thing and only adds to a growing chaotic twisted system of laws that are growing top-heavily. I think its disgusting that people have opinions that subtly destroy our country. Keep your opinion to yourself. Stop trying to hurt others freedoms because you had someone do something stupid and you want to blame it on an external factor that was irrelevent. People can have innumerable distractions besides a phone or a pet... and you're going to blame that when it pops up and call for it to be illegal next.
In the United States it's the opposite: totally legal to throw fido in the car and let them roam free. Except in New Jersey. Go figure.