Why? Because self-driving cars are basically a fleet service driven by a software. Once you remove the driver (where Uber spent so much acquiring) The only differentiator is the consumer facing experience. Neither Uber or Lyft will have as much power as Apple and Google since they ultimately own the mobile experience.
I ultimately envision this business as kind of a Kayak mobile on the phone managed by Siri or Google/Apple maps that will call the nearest taxi or the cheaper rate aggregating from multiple possible vendors. Larger fleets (Uber, Apple, Google) to smaller individually manage fleets. Car companies might decide to also enter that market in collaboration with financial underwriter.
So having a network of drivers ultimately gives Uber some leverage and removing them from the equation, I think it'll actually destroy Uber. This is why I think, this could be a blessing in disguise.