DC Uber user here. A fact that's commonly lost on people: the District itself is actually very small, just 68 square miles. Before a recent fare hike, there was a maximum intra-district cab fare of $19, so a $15 minimum Uber fare is a big deal.

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? ;)