1. You wouldn't need a car per person, only enough to comfortably serve peak demand. There's never a single point of time at which everyone in a city is on the road. (Except evacuations, but see point 3).

2. There is already about one car per person in the US.

3. Automated car fleets would presumably have a cheaper carpooling option, where the car picks up other passengers on the way to the destination. Like UberPool today.

4. Fixed-line transit costs millions to billions of dollars per mile, and easily takes a decade from planning to completion. Building roads takes a fraction of the time and money. And the roads already exist.

Automated car fleets work well for suburbs. But past a certain point, heavy rail train subways have far more throughput than the equivalent amount of cars.

Look at this image for example: http://imgur.com/gallery/v3ff7FY

Building & maintaining roads and highways does take a lot of money too. Building new roads vs building new railroad track on new land isn't that much different cost wise.