This is I think exactly how things will progress and, of course, it is a technology very much still in its infancy and as such will inevitably attract very polarised views. I am convinced that self-driving cars will eventually completely displace human drivers. Their safety record will eventually become so much better that it is inevitable.I doubt we will all suddenly rush out and buy self-driving cars, just as we aren't going to buy AI written books. However, just as we use grammar checkers and other AI to revise and edit, new cars are being built with sensors to automatically prevent such rear-ending. My automatic car with cruise control and lane control already leaves me with little to do. I expect that other incremental changes will eventually result in a fully self-driving car without anyone noticing that it had happened.
And let's be honest here it is a very low bar. Take a look at the statistics for car accidents. We are a race of (mostly) amateur operators of pieces of machinery weighing 1 to 2, or more, tons travelling at eye watering speeds. I can't think of any other regulated, commercial mechanical process with such high levels of danger being permitted with so little training. There were some posts here a while ago stating that in some states of the USA you can get a car licence with pure theory!
However, apologies, I don't want to derail a very good thread to the politics of car driving!