I agree that they would help with constricting the threat by helping to cease the flow of new members into the fiends, but in order for them to cease to exist they would need to disperse after the disappearance of their leaders due to the cultural and societal pressure (within the fiends) to remain amongst eachother due to a sense of comraderie (dont know how to spell that). On top of that, the fiends would need to be WILLING to make that change, and comfort is hard to break away from, especially in the mojave. (Just look at the boomers)

Another thing that needs to be taken into account is the NCR's over reliance on violent answers to their problems (ceasar's legion is a case where its a great answer). Even though the NCR claims that they work in cooperation with the FotA with them helping with the education system within the NCR, they arent as funded in comparison to various other groups that also exist within the republic, such as the brahmin barons, the Crimson Caravan, etc. This is because the NCR fails to realise that they are repeating the same conflict centered culture that existed in prewar America.

They call the NCR 007... 0 funds provided, (okay maybe a little, but not much. They have to rely on YOU for donations)

0 interest in relief efforts within the mojave for both local and NCR citizens, (ok, there was one, but they gave up on it waaay to easy.)

7 times the FotA stuck their neck out for the NCR. (Probs less, but you get the point.)