Almost every non-rural area is going to be able to support the density required. I mean, drive through any suburb and count the number of unoccupied cars.
Honestly, the biggest issue (assuming the technology is flawless) is going to be keeping them clean and maintained because of the very high usage rates.
I think tech people are overestimating how much people enjoy having their own car, as well as driving it. We see everything as something to be optimized, and rightly see driving as a huge waste of time and energy. But, I'd venture to say the majority won't give up their own cars in favor of driverless taxis. Just think about how many people underutilize mass transit available to them in favor of driving their own car.
I think it's just a matter of perspective and whether they are used to the tech, but I can see this technology being deployed in 10-20 years time, by that time older people that don't trust tech will still not drive a car or use a computer, those that wants to own a car would still owns a car, but I bet the majority will hop on this new revenue of personal, car sharing system.
Honestly, the biggest issue (assuming the technology is flawless) is going to be keeping them clean and maintained because of the very high usage rates.