In my rather small city (~600k) there are already like 5 different uber-like options. And at least three of them were before the uber came.
Dislcaimer: I've never used uber and I hope I never will. I dislike them as a company and that dislike grows over time.
Not that it matters, but 600k is not a small city, at least by US standards. Only four of 50 state capitals (Austin, Columbus, Indianapolis, Phoenix) have a population that large.