However, you are right to bring up autonomous cars. I always thought it amusing that Kalanick et al were so anxious to bet the house on autonomous cars, when in fact, they are the company's greatest existential threat long-term. Once those cars are readily available and street-legal, there's nothing stopping Enterprise or Avis or the automakers themselves from becoming overnight competitors.
And once drivers are taken out of the picture, ride prices will plummet. Margins will also thin because of the likely extreme competitiveness of this market. I would not want to be an Uber investor that's for sure. In theory, the "winner" will be whoever scales the most (i.e. has the most capital to put into their fleet) and has the most effective marketing. In practice, prices may be close enough that people will rent car X because they like brand/model Y better.
If I were on Uber's board, I would advise against trying to win that war which they will lose once/if the automakers get in on it, and instead get creative about how to conquer the market in a more niche way.
Someone is going to have to program self-driving ambulances :)