I think it was supposed to visually represent their return to Oblivion (the place). Dremora in TES III were Creatures, not Humanoid, so looting their armor was not the issue. Had they not disappeared, you still wouldn't be able to loot their armor any more than you can loot a goblin's armor in TES IV. In TES IV, the vast majority of Dremora you meet are already IN Oblivion, though some are not.
This could have been the case, if not for the fact that other Daedra types still just fall down even though they still work the same way, if it did, in fact, represent them returning to Oblivion, one would have to wonder why other types of Daedra don't get the same effect.
Ultimately, though, no explanation is offered in lore to my knowledge, whether for why Dremora did it in Morrowind or why they didn't in Oblivion, most likely, Bethesda just thought it would look better than just falling down, and in Oblivion they either decided it didn't work so well, or they just didn't want to bother.