That's in a fantasy premise that will never actually exist.
Back in reality, here's the switching cost: the start-up trying to take Uber's market share, has dramatically inferior data on ride timing/volume; said company has dramatically inferior ride availability in a given city (and at a national, city to city consistency level it's a joke comparison). Further down the line, the upstart is going to lag even further behind due to Uber's data wall, as we shift into autonomous.
Fantasy: it's friction free, anyone can start an Uber clone, there's no switching cost
Reality: it's extraordinarily difficult to compete with Uber, which is why so few have or can. There's a huge switching cost: Uber has all sorts of advantages over a start-up, that help Uber provide a superior service - locally, nationally, globally - over what a new company can manage. Oh yeah, and the biggest one: it's very hard to build what Uber built, it's ten times harder to do it while there's already an Uber, because you have to fight with them and their hyper scale while you're doing it (Uber didn't have to kill an Uber, now you do, good luck).
Wait there's more: and that's before we get to the fact that people are huge creatures of habit. Duck Duck Go produces excellent results, it'll never dent Google's search monopoly in a meaningful way; people do not want to switch unless they either have to, or the context goes beyond an extreme inconvenience. Both drivers and customers will tolerate a lot to not have to go through the immense (to them) hassle of switching. People grow to like their routines a lot, the things they use day to day, week to week; in fact, it's far beyond that, people are hyper resistant to change once they become settled in.