There is very little network effect with Uber. Sure, you can hop off a plane anywhere in the world and open Uber to get a car, but that is a very small number of people overall. I would contend that most people use whichever ride-sharing service is available and most economical in their own city, and if that same service is available on the rare occasion that they travel, then bonus.
Of course, if Uber beats everyone else to the punch with proprietary self-driving cars and undercuts prices profitably, they win. There seem to be some very large issues with that, however.