I know, why would anyone want to play multiple characters? This isn't even an issue for most people, since there's no real benefit to playing alts in this game. I like the class system here, it's great! You can take all the classes and level them in a single character if you want, and switch on the go. I get that.
But there's lots of reasons why one might want to play alts! Lore reasons, and making different characters with their own constructed backstories and such which goes with the classes they main, is but one of many! Owning different apartments in different housing districts to design wonderful looking places, or even getting savage raid gear which apparently can be done on alts to increase weekly loot, which I'm not sure of since I haven't reached that level of content yet. I'm just a sprout!
The problem with this is that it's hard to justify, not just doing MSQ again, which is fine enough since there's a way to circumnavigate it through story skip, but also because equipment is character bound. Not just dungeon drop equipment that you might have for another class you have on another character, but also outfits you bought on store. That's not getting into mounts and minions! There's so many collectibles you would have to collect for every character that isn't account bound, which would make things so much easier.
The problem with this is that sure, even if we made things account bound, we don't have a shared account-wide inventory space. Honestly, why not make the Inn Armoire into an account bound shared space? I can count in one hand the stuff I have that I can put in there, I don't even know the requirements!
One argument I can potentially see against this is that characters can be used as mules for storage space if this is possible. We already have so much inventory space though, with retainers and chocobo saddlebag. Also, this is less a drawback and more of a boon for FFXIV sub upgrades, isn't it? More characters, pay the more expensive sub, more profit?
Just an idea, throwing it out there!