For me, the difference here is clear. When I order an Uber, I have a certain expectation of quality, and I have the option of never using their service if they totally blow it sometime (or I can give a driver a bad rating, and if he/she gets enough he gets booted from the service). If I get a lousy ride from a Taxi, I don't have many alternatives. If a law is passed that prevents anyone else from competing on price, I have even less options.
Anecdote: I live on the far eastern side of downtown, near Penn Quarter, and am able to get from my apartment to damned near anywhere in town for Uber's minimum charge (the major exception being the far reaches of NW, in the Friendship Heights/Van Ness area). Looking back at my history, only 4 of my 23 fares have been more than $15—three to the airport (in Virginia) and one to Tenleytown.
You can certainly blow this argument up if you want to leave the District, but let's be real...who would want to go to Virginia? ;)