You know how a person nowadays can register for uber and drive people around?
In the future, maybe people will register their CAR (which can drive itself). So they sit at home, getting work done, while their car is off autonomously driving itself and picking people up. When you want it to come home, just call it home.
Anyways, you wouldn't happen to have that announcement handy would you?
Anyone could spin up an app that let's people lease out their self-driving cars. The existing ride-sharing consumers are not loyal to the apps.
Until an optimized business supporting lots of cars supporting fewer people undercuts the individual owner on price per ride, sure. Uber with individual driver/owners makes some sense, because you need the individual driver no matter what the ownership structure is. But with autonomous cars, fleet ownership is going to win over individual.