Yes, taxis would be cheaper in a world of driverless cars. But they would still be dubiously clean (perhaps even dirtier without a human there to make the passengers clean up). You would still not be able to leave your crap in them. And they would still be only intermittently available at times of high demand (or else they'll be quite expensive).
In contrast, if you privately owned a car, it would have all its present advantages and also it would be usable even if you intended to get drunk; you could use the time that you were driving to read or use the computer or watch TV or whatever; you wouldn't need to circle around and try to park; you could still potentially utilize the car more than the present situation (for example: your car could drop the kids off at school while you get an hour of work in, and then come back and take you to the office), giving a cost savings.
By the way: does anyone who has kids young enough to require car-seats think that they could get away with a taxi-approach to cars, even if taxis were arbitrarily cheap? Don't underestimate the value of a personally owned car as a mobile receptacle of your stuff.
I don't know which of those models would be more dominant in a driverless car world. They both have advantages over the present state of the art. But I'm pretty sure that the people who jump immediately to believe that the taxi model would become massively dominant are basing this more on their wishes than the facts.