The reason is that you can buy the head piece again from either on the mog station or from an npc. This means that since the item is still obtainable, you cannot put it in the armoire. I know, it is dumb, but that is why it was not added. As for the space, it takes so little room, like kbs of space, to store a flag of what is stored in it that it has nothing to do with why you cannot store it.