The key change for Uber when we have completely autonomous cars is that we will go from a two-sided marketplace matching drivers to riders to a much simpler retail model: riders buying rides. Whatever mindshare and network effects Uber has in the marketplace model will fall in importance, and the new king in the space will be the company that can deliver rides cheapest and fastest.
Uber is way behind Google and even Apple when it comes to calculating the best routes from place to place...