I can only offer anec-data from the Atlanta area, but I know multiple people (including myself) that either sold a car or removed buy a car from their plans solely due to Uber. I've heard a lot of people state they used to risk a DUI driving home now take Uber instead.
It's nothing to do with the app being "so cool", but being able to get a clean car that actually shows up and being able to pay with a credit card. If you call a taxi in ATL, you expect at least a 15-30 minute wait if they show up at all. 90% of the time the driver will be blaring music or talking on their cell the entire ride. Some times they will refuse to take you to places, or refuse to run the meter but demand $xx for the trip. (Happened multiple times to me, all my friends have similar stories.) If the meter is running you have to carefully watch that they don't drive longer routes or even literally in circles (happened to me). And at the end of the trip, it's guaranteed they will only want cash and to take a CC will likely result in a screaming match and attempts to charge extra fees.
When Uber hit Atlanta, it was awesome. A car that actually shows up in 5 minutes? Clean, quiet, with a friendly driver? Map of your gps tracked trip emailed in receipt and card on file charged? The reasons people avoided cabs were removed. I personally take far more uber rides than I ever did taxis, and I know many friends for who it's the same.
It's not that demand for rides wasn't there, it's just there was no supply of quality rides before Uber. Taxis in ATL do not provide an acceptable experience, and are used only if there are no other options. People who before might have crashed on a couch, drove home after drinking, not attended an event with limited parking, asked a friend for a ride, etc. are using Uber because it's easy and economical. I have no idea how big of a percent this is nationally, but among the city dwellers in Atlanta I know of, Uber has been immensely popular and used for trips people would previously avoid with taxis.