You're making an assumption about the armoire that may or may not be correct: that items in it are stored by ID. If they are, then adding things to the armoire shouldn't really be any problem. You'd basically just flag it as armoire-able and presumably the system sorts itself out. However, for efficiency's sake, I strongly suspect the armoire contents are stored as boolean bits, one per item. If that's the case, then to put more items in the armoire, they'd have to increase all user data for every character by a number of bits equal to the number of items that could be stored, a number which will continually increase over time. Granted, it's not actually that huge a number (the Eorzea DB lists just over 15,000 items at present), and I do hope they do something like this at some point, but my point is that it's unlikely the system already exists as you described it.
To go into a bit more detail, let's see if we can get a decent low-end guess of how much space inventory actually takes up.
The items themselves are listed in the DB by hex codes, with the ones I've seen having 11 digits, so that's a minimum of 44 bits. Dye color could be stored as 3 bytes (RGB), so 24 more bits. Durability and spiritbond are displayed as whole %'s but definitely don't increase that way. My guess is 16 bits each for those. I suspect materia is stored very inefficiently, but since there are less than 255 varieties of materia at present, let's be generous and say 8 bits per materia, times 5 slots. Character IDs are past 17 million now, so for safety let's say those are stored as 32 bits. In total, that's a maximum of 172 bits per item, or (rounding up) 22 bytes. The item ID itself is 6 bytes. The result is, if you store four times as many items this way as you have slots, you're still using more data. Not sure if that makes it a good or bad idea, but there it is.