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Your question assumes that Uber's market share as a ride-hailing app will somehow benefit them as a self-driving car company.

Because the car can be heavily utilized by many users, each paying only for the share they use. It's cheaper.

Not having to drive is a very small part of the reason I use Uber in lieu of owning a car. Main reason is expense of owning a car and the time I avoid having to research which car is best for me to buy, how to keep up in its maintenance, where to park, what to do if it's super icy out, etc. etc. etc.

I believe Tesla is planning to have its own network.