In rural areas, an autonomous vehicle would need to travel long distances to pick up and drop off folks. It could be prohibitively expensive or inconvenient. People also use vehicles for other things in these areas, both work and play, which do not fit into the taxi model.
In suburbia, the taxi idea could work, but there might be advantages to owning your own vehicle. Maybe a family will own one autonomous vehicle, just one, but it would be in constant use throughout the day: mom goes to work, dad picks up donuts for coworkers, son goes to school, daughter goes to soccer practice, son goes to track practice, dad goes to get groceries, mom goes to get dinner, son goes to friend's house, daughter goes to football game, mom goes out to gym, etc. You'd have your one family car zipping back and forth between all these events in the family, picking people up, dropping them off, going off to do something else, and coming back again. Having an autonomous car in the family could make sense depending upon the costs.
If driverless cars are a "thing" in the future then what is Uber's USP? Why would you use Uber rather than one of a dozen other companies? Is it just their capital advantage? Their network of now unemployed drivers? Just the name and nothing else?
What is it exactly that keeps Uber in business with driverless cars?