Also keep in mind that the majority of Uber's revenue is from metropolitan areas, not rural areas. And in the metro areas there was a lot of convenience to be gained from their app and matching supply and demand side of the equation and a lot of those areas were underserved by the TLC and specifically car services because taxis didn't even operate there. So they actually took the pent up demand and created a better system.
Now they are still grossly unprofitable, but not for the reason you cited here.