1) Hardly anybody owns cars anymore. When we want to get from point A to point B, we just call a driverless car from the network. But this type of service is a natural monopoly.
When people are ridesharing everywhere, the network with the biggest fleet, becomes the stochastically fastest and cheapest option. Plus add in the fact that they're collecting a lot more data to constantly improve algorithm. This is a winner-take-all market with fat monopoly margins for whoever wins. If Uber prevails, it's likely that their profits will be larger than the entire global auto market.
2) People still mostly own their own cars. They're driverless, but people like the convenience, customization and sense of personal ownership with having their own vehicle. Ridesharing is still an out-of-the-ordinary option for unconventional lifestyles or special occasions.
But in this world, Uber doesn't need to own their own fleet. The same crowdsourcing logic still works. Personal vehicle ownership means a huge number of idle vehicles sitting in people's driveways. Without the pain-in-the-ass factor of actually having to be the driver, expect a lot more people to put their car on Uber's network.