Cars will become more appealing than public transportation over time. As the downsides of cars fall away, their packet switched functionality will ultimately win out, particularly for wealthier people.
If driverless cars eliminated the need for public transport (in the contemporary sense) you could open up rail corridors to create highways for cyclists, joggers, and walkers - it would open up alternatives to motorised travel.
Or you could turn the theory on its head - use the rail corridors as motorised transport arteries and open up the roads to the bipeds.
(From Sydney where the rail network is extensive - I'd imagine places with less ubiquitous rail wouldn't benefit as much)
I would think the reverse. Why own a car if you can get a taxi at your door in the size/shape/color of your choice whenever you need one without having to pay for the taxi driver?
You are right, but I am, too :-). In my mind, a taxi also is public transportation. I do not think I am alone in that. Wikipedia disagrees with it in http://en.wikipedia.org/wiki/Public_transport ("as distinct from modes such as taxicab"), but http://en.wikipedia.org/wiki/Taxicab talks of "modes of public transport" for taxicabs. I guess the terminology will become more confused if/when driverless cars become commonplace.
