For me I am also extremely anxious on the phone (albeit getting better), but this is a niche case.

I think knowing the number is possibly the complication that Uber solves? EDIT: I'm pretty uninformed about this whole world, as I use a dumbphone and never take a taxi so my guesses may be pretty wild here...

Anyway, I suppose that you could have a number that you call that automatically delivers a self-driving car to your location as determined by GPS/voice-recognition technology but I think people would rather use an app.

It's the potential of self-driving cars to make use of this sort of company's services that looks like it'll be profitable to me personally.

And having to explain where you are to people when often you don't know, and having no idea how much it will cost, and having no idea when it will actually arrive.