TLDR skip to last paragraph if you don't want to read my ramble
I've played since Beta and I remember making alts, one to hold provisioning mats, one for alchemy etc. The crafting bag addition was a very welcome addition to the game. Later on the addition of the transmute system also was a big help. I think one of the biggest draws for this game especially in PvP is all of the different gear set combinations you can make but the problem becomes bag/bank/house coffer space.
I'm mostly a PvE player and tank specifically and in this game you typically don't just play 1 class for a role so I have a Nord DK, NB, Sorc, Arcanist, Den and Necro all for tanking. This means all of my tank gear gets stored in my bank because its already incredibly expensive to make. I have Sax, Pearl, PA, TT, all of the Monster and Mythic sets plus off sets such as EC, Drakes Rush, War Machine, Olorime, Crimson Oath etc. In addition I have infused jewelry and Swift for most trial sets because of the different optimizations you need to make for certain Trifectas. No I'm not complaining about having all of this nor how much time and money it takes to get it. I just feel like it is a lot to keep in the bank.
While yes the obvious solution is to just keep it on your character there are too many sets necessary to tank in this game or to heal or even dps sometimes that your bags also become burdened PLUS if you play multiple classes which most people do then you have to farm for potentially hundreds of hours for the transmutes and money to make the gear again for each toon.
Recently I got into PVP after having crafted every single Tank, Heal and dps main and off set in the game and getting a few trifectas. Dear lord there is a lot of PvP gear too and its worse because you often craft the same slot in multiple weights/enchant/trait combinations. While some sets stay on one character only most it makes sense to keep in your bank. Seeing as the gear is all yellow with prismatic enchants on it making it again would cost millions. I've ended up with a bank that has about 350 slots of 480 full of just gear plus 3 house chests full plus alts holding my leveling gear, and random on trait pieces from trial/dungeon runs I'd rather keep than spend transmutes on to make again later. There are very few sets I actually keep on toons. My Alkosh stays on my Z'enKosh DK but Z'en doesn't since sometimes you need it for tank healing vAS. My EC daggers stay on my EC cro but my jewelry doesn't since I use EC for Mini Tank in vCR and Main Tank in vAS.
My suggestion is to come up with some system similar to some other games where you have a gear bag shared among your characters you can take and directly equip gear from or pull it into your character's inventory. This bag could be infinite which I'm sure we would all love or more likely would be something to do with ESO+ and/or Crowns so that ZoS can make some money as I'm sure they will want to do. In the end I know that most of the end game player base is more often than not playing managing their bag and bank space simulator more than ESO itself so it would be a much welcome addition to the game.