Yes, I'm in a medium-sized city in the US. Uber and Lyft operate here, but they don't seem to be as popular as taxi companies (at least, I see far fewer of them than taxis).
I know that two of the largest taxi companies in town have just increased the number of drivers they have.
In my city, taxis have responded to the presence of Uber and Lyft by matching what they do, and taxi companies are thriving.
Aside from the stupid "rating" system and the price of the trip, there is nothing Uber or Lyft offers that isn't matched by real taxi services here.