This isn't a Bug rather that it's an "Oversight" and below will be a "Suggestion Tie-In"
If the Story's Exposition for providing the Arcanum Apartment is that we'd need a place to stay within the Arcanum to continue pursuing our Arcanum Understudies easier and have more direct contact with the Teachers/Associates of the Arcanum after we've graduated from Ravenwood Academy in Wizard City, then...
Why are we allowed to delete the Arcanum Apartment from our Inventory?
Especially considering that a new "Musicology" teacher has moved in across the hall from us, guarded currently by a Lumi that seems to like Nana's Chocolates and promises to deliver the Chocolates to the Teacher when they show up, owning the Arcanum Apartment should be that much more valuable to the Player.
The Arcanum Apartment is also listed as "No-Trade" meaning you can't Trade it back to your Main Player, either.
Since the Arcanum Apartment was so important for the Player to own that the game gives it to you in your Main Series of Quests, Players should EITHER be UNABLE to delete/sell/trash the Arcanum Apartment for ANY reason (Similar to how you CAN'T do anything with your First Pet from the WC Quest that sees you fighting Old Judd to free some Pets in the Olde Town Tower OR the Beastmoon Planters)OR be allowed BACK IN their Arcanum Apartment by simply walking back in the Apartment's Front Door in the Arcanum, therefore re-adding it back to your Inventory (Kingsisle can figure out a way to cover a loophole of people reselling/trashing their Apartments over and over again, perhaps Ignus or someone in the Arcanum can sell the Apartment back to you for 100K Gold?)
Seeing the value in the Arcanum Apartment, I'd also suggest that it get some more backstory and benefits. (Perhaps an NPC that once previously lived in the Apartment or a random NPC (Like a Lumi) can cite that there is a downstairs part of the Arcanum that hasn't been touched in Years, allowing the Player to access a secret downstairs level of the Apartment OR an NPC cites that there is another type of hidden secret or background lore to the Arcanum Apartment)
