The first company to provide a total and credible alternative to a human driver will probably capture most of the market. There is little reason to believe this will happen precisely simultaneously. Even a relatively short lead could be a massive advantage.

Also arguably the company providing the contact with the customer is more of a commodity. Certainly its the easiest aspect to replace. 100 companies could handle that tomorrow with existing tech for example. I can imagine people using a service that shops a bunch of car services and lets you connect with any of them.