The problem with shotguns is that you either have a small number of pellets (12ga) or a small amount of mass to do damage (bird shot). So with 12ga specifically, while it's more effective than a rifle round -- the pellets spread quickly enough that it's only a huge advantage when the drone is in the terminal phase. This is why in WW2, they would put timed fuses inside the AA shells so that they didn't have to hit the aircraft directly with the shell but the round didn't spread so far that it was useless.