I spend the bulk of my time in this game micro-managing my inventory. I've got my research items, mats for 6 different crafts, as well as all the world drop gear you have to deconstruct, which spawns even more mats. I've got about 40 treasure maps floating around, some ultra-rare set items I'm waiting to use and a few cosmetics.
Some people want the limit to just go up, others think materials should be exempt, or have their own space. Zenimax has come out and said that the reason for the low space is that they don't want every character to do every craft. This is also obvious from the lack of skill-points in early game, where too many points in crafting will likely cause the player to come up short in combat.
/Constructive
Proposed Solution
Give every craft a new three tier passive. Called something like, "Blacksmiths Backpack", "Provisioners Satchel" or "Enchanters Bag".
This Passive gives the player an ability to carry around +3/+6/+9 extra materials in the profession the points are in. These inventory spaces are usable only by a select number of materials, and encourage the everyday player to collect world spawns, rather than resenting them as something that will send them back to bank again sooner. This still works to move people away from doing 6/6 crafts on one toon, as it is expediting the skill point stretch in early game.
I think having this passive act on the bank would be another positive thing, and potentially stacking for every player character that has the passive. It could cause some slight interface issues, but I'm sure that you have the skills to fix that one up. At the moment, bank space is solving some issues (which may or may not be a problem in the first place) but causing many bigger ones, and drawing people away from playing the game and experiencing the lore, to working with a dull and repetitive bank situation.
Constructive/
/Rant
It just doesn't add up. They say they want to discourage players from doing all crafts on one character, at least straight away. OKAY, I can deal with that. So, I've got 2 main toons. One does the three stock standard crafts (WW/BS/CL) and the other one does what are in my opinion, the more eccentric crafts (EN/PR/AL). Cool, makes sense. They are both end game (VR12/VR7) and have a large proportion of the skill points in the available. At the moment, VR12 has to hold all of his mats in his inventory, because otherwise there isn't enough room in the bank for VR7 to go out and quest with a near-empty inventory. If I want to get back and do some trials on my VR12 I have to go onto my VR7, withdraw a heap of crap from the bank, then deposit everything on my VR12. To switch back I have to repeat this 10 minute process and pray I don't screw something up and extend the already frustrating ordeal. I have followed the play style they want to draw us towards (which is an issue in and of itself) but they still slap me with boring time and inventory penalties at every turn.
Oh, and then there are cosmetics. So many quests spit out these cool little gadgets that make you glow funny, or turn you into a skeleton, or give you a little pet. Great. These could be fun to pull out at a guild party or something, spice it up a little

But to do that, I have to have it sitting in my bank, taking up a space which I really need for that other alchemy reagent. So every time I get one of these things, I just destroy it straight away. It is just going to add to my inventory management Woes.
And don't even suggest that I should be making a bank toon, while I enjoy playing my fat, old, pasty nord... it isn't a good mechanic. It adds even MORE time to my bank run. And I already have 2 toons well into endgame after 2 months. I know that at the very least want to run 2 more in to have a character for every class. Then what happens? What if I want to make some friends in a different faction, run another race or try out some different focused builds? Bank toons are unsustainable and not a fun part of the game. They are *NOT* the solution.
Rant/
/Response
/Opinions