A self-driving car would not necessarily be great for Uber. What is the taxi service currently providing? A way to order/pay for/sell a cab ride, and vetting so you don't feel uneasy with the driver.
Take out the driver, and anyone could offer their car as a cab. The app to do so could be Uber, but it the bar is lowered considerably if it's purely a way to book a car.
However it would be a capital intensive business, and Uber has the capital. Uber also the brand, the customers, the data, and a bunch of robotics experts. They also seem to be really good at operations.
The two things that are a knock on Uber today are the politics around taxi licenses and the politics around compensating their drivers. I can see why Uber would be happy to eliminate one of those problems.
If I'm leasing out my car and I'm not going to be in it, I'm going to care a lot more about passenger vetting than the passengers are going to care about vetting me.
Take out the driver, and anyone could offer their car as a cab. The app to do so could be Uber, but it the bar is lowered considerably if it's purely a way to book a car.