The wardrobe actually requires only a fraction of the space that other kinds of inventory do. This is because the wardrobe ONLY keeps track of the type of item. Modifications to the item, such as dyes, glamours, and wear-and-tear, are not recorded (this is why you are warned when storing the item that such things will be lost, and that the item needs to be repaired to 100% before it is stored). Because it only stores the type of item, the item's identification number is the only thing that needs to be tracked. Also, since the wardrobe can only be accessed in very specific areas, like the inn, it doesn't have to be loaded from the server every time you change zones.
Adding additional items to the wardrobe is probably the most low-impact way SE can increase our inventory.
THAT SAID, the wardrobe is intended for a VERY specific purpose: allowing the user to store items that they can't obtain a second time. While it is true that many items in the wardrobe can now be obtained from the Calamity Salavager, back when they were first added to the wardrobe this was not the case. If you threw away your artifact armor, it was gone FOREVER. If you threw away your horse kabuto, it was gone FOREVER. This made players want to horde these one-shot items, eating up precious inventory space. To ease this, the low-impact wardrobe was added so that players wouldn't feel pressured to hang onto them.
Primal Weapons, on the other hand, are NOT one-shot items. It may take some grinding to get the one you want, but if you throw it away, you can always grind again to get a new one. For this reason, I doubt primal weapons will ever be added to the wardrobe. The same goes for other items players worked hard for, like High Allagan gear. They may be hard to replace, but they're not IMPOSSIBLE to replace, like artifact gear and the event items used to be (and, in some cases, still are).