The sloth demon kinda already has that domain, if you remember how it tried to give all your companions what they desire in the Fade quest. Its goal is just a little different in that giving them what they desire is only a means to induce sloth.
Well not really. I doubt wynne's desire was to be surronded by dead children. Or shales desire was to be trapped immobile forever. Or morrigan to be stuck with Flemposter. Or Zevren to be stuck on a torture rack reliving his initiation to the crows. Or oghren's to be stuck as a mockery and a joke in orzumar.
See what I'm saying here? Their physical bodies were stuck in the real world catatonic, and it had desire demons working for it, or one at least. The whole illusion thing isn't something exclusive to sloth demons mind you, but its method of leaving you catatonic while trapping your mind in the fade seems to be its true MO.
Desire demons work less on the principle of imprisonment and more on the principle of bribery. And since bribes can be many things, so too should a desire demon be many things at once. In fact all of the demons should really, rage demons, sloth demons, and possibly hunger demons as well, seem to all have this philosophy in their designs, but not desire and pride for some reason, which are one of the few with distinctive models.
At least until DAI comes out and gives everything a unique form I guess. Though I'm not complaining, the more the merrier I say.