> majority of car owners are likely to want to keep their cars for themselves.

I can bet that in most big European cities, relying on public transportation + renting a car whenever you need is cheaper than the maintenance costs of car ownership (parking + insurance + gas).

Making the car rental more efficient on a global scale will reduce the need and the utilitarian value of car ownership. There will be of course those that will want to have their own car, but that will be more and more considered a luxury item or status symbol than a need for anyone living in urban areas.