I'm a single woman who doesn't own a car, and I won't use UBER for a number of reasons.
Like most Americans, I don't have a smartphone. I have a small child, and I'm home or at work a lot, so my computers provide adequate connectivity.
Just because the US Attorney chose not to charge the driver in the DC case, doesn't mean an assault didn't take place. This isn't the first time that an UBER driver has been accused of a violent crime.
http://www.huffingtonpost.com/2013/03/12/dc-uber-lawsuit_n_2861451.html
A licensed cabbie in DC has had a criminal background check. They have a posted license in their cabs, and I check the driver against the picture on that license when I get into a cab. UBER just contracts with other car services, and I have no idea what kind of background checks they do. In fifteen years, I can't remember an unpleasant incident with a DC cab driver. However, I've used limo services a couple of times, and I've had drivers ask me uncomfortable questions. I think some of those services are family businesses, and they won't fire their relatives.
Taxis are what economists call a experience good. You can't observe the quality until you purchase the good, and it's difficult to use the discipline of the market to ensure quality. UBER may have a driver rating system, but using that alone and not regulating the system is like saying we don't need a Consumer Product Safety COmmission; we can just use Amazon's customer ratings.