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I'd say the big barrier to more cars is cost, not being unable to drive (particularly in big cities).
Think of how much an average car is used in relation to it's value ie £/hour.
Now think about the changes in how we own and use things nowadays.
Driverless cars would go hand in hand with an Spotify-Uber-style system. If cars were utilized to even 50% of their ability then the cost would plummet to an almost meaningless level.
The alternative scenario is that when you have cars that can park themselves and come and find you we'll end up with something more like a glorified taxi fleet.
I'd say the big barrier to more cars is cost, not being unable to drive (particularly in big cities).