Then the miles I put on my car are from my use for my pleasure.
When you can just ask for a car to pick you up and one will arrive, corporate robo-taxi fleets will have economies of scale over family cars sent off to earn their keep. With ordinary people not needing to buy a car, facilities for maintaining and supplying them will dry up too, as the manufacturing effort shifts to taxi-ready cars for fleets. And the price will shift up out of your range to reflect the earning potential.
The robo-car will end the private car as anything but a hobby comparable to the classic car.
Robo-taxis have an economic attractor at the "runs forever, gets good mileage" end of the design scale, because energy and maintenance are the biggest ongoing costs. There would be incentives to make them small and efficient, maybe sized for one occupant. And they would not sit around idle, so they would need a long MTBF, which rules out designing for speed or beefiness and suggests electric (it's got fewer moving parts).
All of which means, fewer, smaller, cleaner, slower, simpler, vehicles. Aesthetes will pine for the days of muscle cars. In terms of green-ness, they may come to eclipse buses etc, while retaining the advantages of cars (goes where you want, when you want, and is not full of strangers).
It's also worth noting this type of service is only effective in dense urban centers. Enough people live in the country/rural/suburban areas where owning a car is necessary.
Americans spend a ridiculous amount of money on cars as status symbols. It'll be a long, long time before that ceases to be the case.
Maybe you meant the robo-car will end the private car in cities where its citizens focus on different status symbols? I can see that being the case in SF and maybe NY in the near future, but not anywhere else in the US.
This is sort of the whole point: everyone thinks they can eat their cake and have it too.
DUI? I'm not the driver, the car is! Hic!
Run over a kindergartener? I'm not the driver, blame Google!
Auto insurance rates go through the ceiling because of untested technology? Wait, I'm the same driver I ever was, this is unfair!
Can't get insurance at all? Help, the Man is a luddite! I'm being repressed!
So, "The Man" in this case is a luddite, and making laws that require humans to be in control of the vehicle actually decrease public safety.
I don't mind public transit but I'd much rather be driven around by a cab.
The great thing about an automated fleet is that you could actually switch cars during the journey. Take a small car to leave the busy urban areas and than switch to a larger car when you get to the motorway.
Likewise, it may not be possible in the short term to convince everyone to stop driving cars. Self-driving cars won't fix the long-term problem of efficient transportation, urban sprawl, or emissions, but they can reduce its harm by efficiently providing car-like service to the public.
Hey, there's a start-up idea: Buy a fleet of these and deploy them around the Bay as the Robot Cab Company. Have them queue at designated points or hailed via smartphone. I expect to see this at Y-combinator in 3-5 years.
Now, if we could only wedge a social networking component into it...