I've been driving for Uber for about nine months now, part time.
While autonomous vehicles seem like a natural fit for this service, I can say from experience that about 30% of the pickups are set by the passenger at a wrong location, and require some driver / passenger interaction in order to actually find the rider and make the pickup. With the driver out of the picture, many of these will trips will likely become a "cancel - wrong address" and re-request, adding to the pickup time. I don't see any practical way for an autonomous vehicle to work out that Peggy isn't actually standing in the middle of the mall - which is where she set her location - she's really outside the Verizon store at the curb, waving frantically.
Further, how will vehicle condition be managed? How will they insure the vehicle is clean and ready for the next passenger? Free of vomit, personal property, not vandalized? Will each vehicle be monitored by a remote Uber employee from a concrete bunker in DurkaDurkastan? If so, then we're right back to the human employee problem set again.
Seems like they'll be trading one problem set for another.