But does Uber really have a competitive advantage here? In the multiple cities I have lived in in the past couple years (Boston, Austin, Dallas) I have never noticed Uber's range being greater than any particular taxi. I do prefer uber do to brand trust, but I had no issue switching to RideAustin after uber left the city.
They may not go where you want, they may not be available where you are, because you are not in the right part of the city.