Some of the same items are used by different classes, so what would you want them to share those items between multiple 'store bags'? How can one item be in multiple places at once? Maybe if you split them, but then you would still have to change class and move around items yet again.

We're given a limit of item slots to begin with, what you're suggesting would basically break that, seeing how we'd only have to worry about dark matter to repair, food and HP/MP recovery items, maybe some medicine for spiritbond/durability bonus. And if you have a 'mess' on your character/retainers, then I suggest to take the time to sort for items, or perhaps sell some stuff that might just be collecting dust and let someone else put it to better use?

Plus I'm a bit confused in why you're bringing this up, when you just scratched the surface of crafting? (Also might I add that having Alchemist as your first 50 will clutter up your item bag and more, they need a massive range of items to make much)