A while back someone suggested adding a diablo style rift system to The Division but it would be a skyscraper where each level has progressively more difficult mobs.
Honestly I think it's a great idea and I LOVE how in Diablo the mobs drop no loot in greater rifts because it puts more focus on timed runs and less on picking crap up.
as with everything else that is wrong with this game, it will depend on what type of reward they have waiting for you at the end of the tower. If its 1 piece of yellow loot you can guarantee nobody is going to do it past the first try.
Fix the loot system and the devs mentality about loot FIRST .. then worry about adding in more ways to get said loot.