Currently both Uber and Lyft handle the task of vetting drivers and making sure there is a good experience for their customers. They organize and control the labor required for a good experience for the riders.

Think about a rider in a world where Lyft and Uber are both dispatching self-driving cars. What's the difference between the services if they're all using Mercedes S-Class SelfDrivers? The rider knows that all Mercedes S-Class SelfDrivers are the same experience. There's no question of if the driver is trustworthy or competent. Uber and Lyft would be providing the exact same commodity experience of sending a self-driving car to your location to then do your bidding in exchange for money.