I would say that since the majority of mules don't have access to sky/sea the aspect of actually trading said items might not make sense since they have no means of obtaining those items if you are referring to the rare/ex versions. By allowing people to trade said items to mules it would encourage people to horde loot rather then have their fellow allies hold onto it.

Consider that you can put loot in your d-box then have it sit in the recieve box without having to grab it. So techincally you would be able to horde 8+ of the same pop item if you wanted to for sky/sea. I"m pretty sure that's the consideration they took into not allowing those pop items to be delivered through the delivery box.

As for abjuration if you are giving it to your "mule" to get them a piece of abjuration then that means they must be strong enough to do it themselves so why not just go as that character to get them. By allowing abjuration to be d-boxed you run into the same issue that people might horde the abjurations for themselves instead of letting it go to those that might need it.

So basically the reasons those will most likely remain undeliverable is because by allowing them to be delivered to another character you leave the door open to allow RMT to stockpile said pop items and sell them as they please which may cause said RMT to pidgeon-hold certain events because they aren't limited by the rare/ex aspect of the item anymore.

As for things like empyrean gear that is a different beast. While sure it can be said that people might get it on one character then use it on another the items in question are more plentiful and the aspect of being able to trade said items is to relieve the time sink if you do happen to have another character on the same account that needs said item but no one else needs it. Abyssea has more options to obtain said gear while things from sky/sea and abjuration mobs are a single NM that's either timed or popped depending on the conditions.