I don't think that the main problem here is that the perks are what make a weapon op but what its base stats are that make the difference. All the wepon perks that are in game are not meant to give a weapon op stats, they are there to give it a little bit of an increase which shouldn't make it a game changer (unless it is an exotic). even with bad perks shotguns like Party Crasher and Felwinter Lie were still very strong. If I were to look at it on what can make shotguns more fair it be good to make it so that at close range without precision damage it just brings your shields down. This way it would truly be a weapon that compliments melee like in Halo when you use the shotty to being shields down then melee them for the kill.
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^^^ this to the letter "T" Even without perks those shotguns were ruining riot in crucible.