The problem with shotguns in the crucible is not range. It is that they are one shot kills that don't require much skill. Adjust them for crucible (leaving PvE alone) so that it takes at least two body shots for a kill (one for a head shot which would require skill and being very close) and it will solve most of the problem. Bungie just does not have a damn clue. Side note: Crucible is worse in nearly every way because of the crucible based quests, no incentive to stay in a match, etc.