SE doesn't want to be bothered by all the players who would discard them and then change their minds later and whine and fume about the inability to get them again. (Maybe this isn't you, but plenty of such players exist for that to be a legitimate concern.) So any item which cannot be gotten again and which doesn't take up storage space to keep is marked as non-discardable. Just put it in the Armoire and then ignore that it's there.

(I'm equally certain that I'm never going to want to wear a giant chocobo head, but I've got that there, too.)