Just because a driver has their hands on the wheel doesn't mean they're watching the road. They might be watching a movie.
As for asking about number plates - that sounds like a distraction that would cause accidents rather than prevent them.
For me these systems need to be really clear. Either the person is driving, in which case they are fully responsible for every crash, or the car is driving, in which case the car is fully responsible. There's no room for any grey area in the middle.
In my opinion Tesla should be forced to refund anyone who was told their car has "full self driving". I'm OK with autopilot though, since the airplane and boat version of that feature has always pretty much been "just keep going in a straight line until a human disengages autopilot".