You can mail them to the literal same character, effectively letting you float gear/supplies/zeny for however long the expiration timer is.
example: About to go to ET -> mail yourself 750 pots + 250 acid bottles and 250 bottle grenades -> resupply from mail when both are low -> don't need kafra card or to walk back up to top floor.
or: Overburdened but don't want to waste time (gum, battle manual, etc.) -> write mail to yourself and send 2,000 weight's worth of things that you can retrieve later (flywings, healing items, etc.).
It's also a lot easier to just leave one char at storage and mail yourself the items you need instead of moving back to storage over and over. I foresee great ease of use from the system.