Eeeeh, in the long run I think it'll just become unnecessary to own a personal car for most people if self-driving car fleets become a thing - I dunno... it might be a luxury like owning your own boat, if you're vacationing on a lake you can always rent one so why pay to maintain something you very rarely need... more apt might be to consider it equivalent to owning your own train car.

At any rate I don't think personal property ownership should be made illegal, it could just be made to cost - taxi companies are taxed for running a fleet of vehicles and charging people to ride on them, that sort of mass property ownership could be similarly taxed.