Since most people have alts and their storage mechanism why not make use of it through the housing system.
When your alts are in your house you can access their inventories from any other character sort of like the bank. The bigger your house the more alts you can access. Ideally they could make it so your alts are physically in the house and you could click on them to do this.
There is your storage and reason to get a larger home without actually changing much.