What you describe is a car service with an automated driver. Car services have existed for decades, and saving $20-25/hr on a driver isn't really that big of a net gain. The biggest innovation Uber offered is app-based dispatch.

There is a lot of skepticism that automated vehicles will ever happen without massive infrastructure changes that remove human drivers from the road in large numbers. The liability issues are huge -- accidents will happen and people will die. In a case where fault must be determined between an autonomous vehicle and a human driver, human judges / juries are going to overwhemlingly side with the human. If anything, automated vehicles will require more costly regulation than human drivers do.

Car services are a hard business to make money in because the job isn't very skilled, so there was a lot of regulation in place to ensure those services were priced in such a way that they continued to be reliable. Uber sidestepped a lot of that regulation through creative accounting and VC subsidization, but my guess is that when Uber and Lyft implode in a year or two, much of it will be reintroduced to fill the smoking hole they will leave in last-mile transit since they put the taxi companies out of business.