I know nothing about Uber's business plan, but I do know that self-driving cars are poised to change not just the vehicle and the way we drive (or are driven) but the entire paradigm of personal transportation. When a car can pick you up at your door, drive you to the door of your destination and then go away and take care of itself, owning a car is more of a headache than a convenience. Why deal with parking fees/garage space, maintenance, fueling, etc, when you can push a button, get exactly where you need to go and pay one simple price, whether single-time or subscription-based, without the hassles? And if people stop buying cars, Uber, with its loyal user base and brand recognition, is much more than just a modern taxi service, and that fleet of self-driving cars doesn't look quite as expensive when compared to the potential profits as it does inside today's driving paradigm.
Subscription models are already starting. A month ago Hyundai announced that the upcoming Ioniq Electric will be offered in a package that's like a beefed up lease: leasing costs/unlimited mileage/charging costs/regular maintenance/wear+tear parts/registration/etc. I believe one of the luxury brands is experimenting with or preparing a subscription service where, instead of leasing a specific car, you pay a subscription fee for on-demand-style access to a whole fleet - get a sports car when you're taking a fun drive, an SUV when you need to pack up gear, a sedan when it's a family outing, etc.
Expect to see more changes like that leading up to self-driving cars and an explosion after. Will change the entire business landscape for something like Uber.