I haven't found a comprehensive list of all Dressing Room equipment- so I come with a question!
Can an Alpaca Robe be placed in the Dressing Room?
Even if it doesn't fail the rules, you can test this by opening the dressing room, go to whatever tab (robe in this case), and search "Alpaca" as exactly as you can. If all the boxes disappear, or none of the boxes that remain are the ones you are looking for, then it cannot go in the dressing room.
So why are irrepairable items an exception? I get why untradable is but not irrepairable.
You do know they added a second check a while ago to check on in order to collect the items.
I do get both part on why they won't make irrepairable and untradable not storable as well... They won't allow you to store an item if it have 0 dura.
However... Like Esileruf said... The 7th Anniv. Hat are repairable but not tradable... However, it can be traded between characters via bank and/or pet, so it still meet the rules and thus they consider it as a collectible item.
The general rule is if it cannot be repaired or traded, it cannot be put in the dressing room.
The alpaca robe fails the latter. The only exception is the 7th Anniv Hat and I believe the Maple Dress/Suit. I don't remember the unique interactions.
I don't believe it can be put in a pet, but untradable generally never disallowed bank transfer. A big case-in-point is many of the swimsuits, the Yukatas, and irreparable JP/KR-named items follow suit, but aren't able to be placed into the DR.
I believe you can put the hats into the pet as well... I have tried it when we had the 7th Anniversary event. The hat are just not tradable into different accounts.
Maple suit can't be stored. I've tried.