They actually do. The NCR, with the help of the Followers, got the Hoover Dam up and running again. They were also the ones who pushed the Legion out of the Mojave at the First Battle of the Hoover Dam in 2277. They also as
@Crni Vuk said have settlers and businesses in the Mojave like the Gun Runners and Crimson Caravan. While House dislikes the NCR's democratic government for the same reason as Caesar, viewing it as doomed to repeat the failures of the Old World, he nonetheless see's them as valuable trade partners and a good distraction for the Legion.
Look, Alec isn't here anymore to be the resident crazy person. I feel it is my job to fill in his shoes!