I personally don't see it. Uber has already begun being disintermediated. For example, ride-sharing is already an option in Apple Maps on iOS where Uber sits alongside Lyft and any other ride-hailing apps on your phone, price comparison and all. You can also hail a ride with Siri. As a rider, why would I care whether my ride is dispatched by Uber or Lyft? I only care about availability and price. At some point in the future, I probably won't even need to install a competitor's app on my phone; I'll ask Apple Maps or Siri to get me a ride and it will dispatch a car from whichever service is faster and/or cheaper.
Uber has a plausible route to winner-take-all dominance as long as ride-hailing remains a two-sided market, where competitors have a chicken-and-egg problem in recruiting drivers and riders. But self-driving changes the game.