With the inventory system being a real nuisance and limited, the Armoire should be able to store more relevant equipment items and some of which aren't able to be stored which doesn't make sense.

Can't Store:
Seasonal Gear - Summer Evening Top and Trunks / Striped Summer Top and Trunks

yet you CAN store, Red, Green, Blue, Solar, and Lunar versions.

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Can't Store:
Exclusive Extras? - Patriot's Bracelet

Can Store:
Exclusive Extras - Patriot's Choker

They are both functionally the exact same items just on a different slot, yet one can be stored and the other can't, which makes no sense.

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Other things like the Moogle Cap, Starter Gear, or even the Lv.5 "job" armor can't be stored in the Armoire and yet they sure seem like things that should be able to be stored.

In the case of the Moogle Cap and Lv.5 "Job" armor they are even non-convertible and unsellable. So your only choice to get rid of them for space is to discard them which don't seem like things that you should have to do that for, at least compared to being able to store seasonal event swim suits.