What, why? There's no winner-take-all aspect to shuttling people around. Taxi service is a commodity and taxis-without-drivers will also be a commodity. The switching costs for users are essentially zero.
That's how we get Uber, Lyft, DiDi, Grab, Bolt, WeRide, BlackWolf...
I don't know how you can write that list and come to the conclusion that it's not winner-take-all. In their home market (US), Uber is ~75%, Lyft is ~25%, and all other competitors are sub-1% combined. Didi is similarly dominant in China, and so on. "Completely different markets have different winners taking it all" does not counteract the claim of winner-takes-all in any way, nor does listing utterly insignificant players like BlackWolf. Do you think people saying "winner-takes-all" in business contexts mean one company with literally 100% marketshare globally?