Multi-car families extend that rational by having two or more people that need a vehicle at the same time for different purposes with different destinations.
That is not going to change just because there are driverless cars.
Driverless cars mean that you can commute to work. Once you're there the car THAT YOU OWN can then head home and pick your kid up and ferry said child to school.
What will happen in time is that companies/schools/whatever will get a little more flexible with their start and finish times to allow this to happen.
You may wish to own your own car, probably a long term lease rather than own outright, and that will still be permitted.
It'll just cost you more than pay per use unless your family usage pattern make the cost worthwhile.
But imagine if a company like Uber is running all this? Yuk.