I can see self-drive motor vehicles eventually being banned from public roads. If auto-drive is two or three times safer, why would governments accept the ridiculous death and life-changing injury toll on our roads. Land transport accidents are the leading cause of death in British 5-19 year olds (a tiny minority of which are non-motor vehicle related).
I think that private ownership of motor vehicles will fall, as people realise they can book a motor vehicle, and for a premium, summon a vehicle at short notice - furthermore, they will be able to book their vehicle according to their needs: Smart type cars for individual people, family cars for families and sleepers for longer journeys. Cycling will become even safer, and people will own pedal bikes and electric bikes and use them as utility vehicles for short journeys. Trains, outside of large cities, will fade and railways go the same way as canals.
Enthusiasts, and the wealthy, will still own their own auto-drive vehicles. And specialist auto drive vehicles, like campervans, will still largely remain in private ownership.
Self-drive events, like the Veteran car run, will remain on roads temporarily closed to auto-drive traffic.