might: Strong push?
"The end of private personal transport, the start of a new public transport system.."
I can't see it happening. What about farmers and other people who live outside of town and the types of vehicles they use. Are you going to have driver-less tractors? They certainly won't be hiring one as they are needed, I suspect. Too useful NOT to own one. BTW I wonder how good autonomous cars would be on gravel back roads, with random potholes and/or loose gravel lying around.
Not to mention tradesmen who keep their tools in them, might use a driver-less vehicle, but probably not rent them as needed, unless someone comes up with a "pod" system that contains the relevant tools, which can be attached and detached very quickly.
I am currently doing copious landscaping on our land, and that involves going to the timber yard, attaching one of their free trailers to transport 1 or more pieces (depending on what I need at that moment) to home. It would be impractical and expensive to have someone deliver a single length of timber. As the project is being designed as a I go to suit the land form (steep) there isn't much possibility of advance planning and buying all the timber in one go.
Having said that, although I like driving, I would still use a driver-less car for certain journeys. E.g. instead of taxis,, but they would have to be available when I want them, and a hell of a lot cheaper than our current taxi prices.