Nah, you don't need to ban anything. Just force the rule, that if company sells self driving, they are also taking full liability for any damages of this system.
By this logic, then we should also create a rule for regular, non-self-driving that says, if you have a car accident that kills someone, all your wealth is taken away and given to the victim's family. If we had a rule like this, then "you'd probably see much safer driving". Are you willing to drive under those circumstances? I am sure you will say yes, but it does not make your suggestion any less ridiculous.
We cannot even properly ban asbestos, expecting people to die first is just having a realistic perspective on how the US government works WRT regulations.
That's a legal non-starter for all car companies. They would be made liable for every car incident where self-driving vehicles were spotted in close vicinity, independently of the suit being legit. A complete nightmare and totally unrelated to the tech. Makes would spend more time and tech clearing their asses in court than building safe cars.