I have a hard time seeing that as an endgame that Uber is well-positioned to win at.
Right now, Uber's core competencies are having a nice app, and managing a bunch of people-centric things like recruiting drivers and getting them to be available to drive at times when people want rides. Of those two, the latter is probably the more difficult one to clone. It's also useless to a company that doesn't employ any drivers.
What they have close to zero competency in is fleet management. That's something for which traditional cab companies have something approaching a 100 year head start, and they which are very good at.
I think that's the reason why Uber has decided that it's so critical that they develop their own self-driving car technology: They need to control a supply of self-driving cars during the critical transition period if they want to avoid being at a disadvantage while it's happening. If everyone's buying commodity self-driving cars from a big automaker, then it's just a game of who can operate most efficiently in order to offer the lowest prices. Traditional cab companies were already good at that, and, if anything, the influence of Uber on their market over the past however many years has forced them to get even better at it.