The game theory isn't really winner take all. In a two-sided market like Uber (drivers and passengers) it's nearly impossible to bootstrap competition, but with autonomous fleets it's just a matter of capital. You can dump 100 vehicles into a market and be a local player pretty quickly, and the between-city efficiencies aren't super important.
Developing the tech is getting cheaper too (sensing hardware improvements, ML improvements) so the first-mover advantage likely won't lead to stable moats. Competition will be more like Apple/Android where constant improvement (probably on cost) is necessary to maintain a lead.
We're setting up for the biggest "winner take all" product-market fit in history.
Besides, ~99.9% of people won't have the expertise to make an informed decision on which provider to use (if they even have a choice).
The only losing scenario is if one is particularly bad, leading to a ton of regulation (like a FAA for SDCs).