Of course it's possible to build some app that tells people nearby to pick them up with metering/billing services built in.
From a business standpoint, it would almost be impossible to duplicate what they have today.
Ultimately, this space will operationalize out to the company that can manufacture safe and reliable self-driving cars most efficiently. That's kind of how you can tell uber hasn't won yet: if a company came along that was doing that, it would eat their lunch.
Further, faced with the awesome self-driving car company, uber's hungry huge capital needs thus far will be nothing but a burden.
I believe they timed this all wrong -- they are myspace and in the wrong business.
Assuming, of course, the fleet cap- and opex makes autonomous vehicles a more profitable proposition than driver share without fleet costs, and it gives them a competitive advantage over smaller autonomous taxi fleets. I'm curious what their internal projections look like in that regard.
If someone can get the cost down to 1/10th or speed it up 10x etc, then uber may find itself down and out (or racing to catchup).
i.e. I could build "the Uber for when you want to go out on a date and impress someone in the car" as an overlay service.
There is a service for that. It's called Uber Black.
"The most common cause of failure in leadership is produced by treating adaptive challenges as if they were technical problems" - Ron Heifetz