This, in itself, is very annoying (to me at least). Why do we have to go back to the White House or Haven just to switch our Specialization Weapons? They're in our inventory, so in reality all you have to do is just equip it. In the game you have to go to the White House or Haven and activate the Specialization just to use the weapon. It doesn't make any sense to me whatsoever.
Please allow players to equip either the Specialization or the Weapon on-the-fly. It would be super convenient and a good QoL update in my opinion.