I'm not sure how many years its been since the pets came out that gave you extra bag storage for your characters but its been quite a while. There have been constant new sets released and the incentive to make multiple sets and swap them between characters almost seems intentional by ZOS. That said I can't be the only one running out of bank and housing storage for my gear. I tank on all classes except plar, dps on all classes, support dps, and heal on all relevant healing classes for pve and into trifecta content. I also PVP. That said with trifectas there are a lot of niche sets you are expected to run, in pvp there is a PLETHORA of set combos and don't get me started on tanking and healing sets. I did the math the other day and I have around 600 pieces of gold equipment.
The transmutation station was a godsend but I can't exactly break down my gear once I'm done with it as that would be throwing the money in the trash used to upgrade and enchant it. The housing storage is also nice but its also very hard to manage since the chests are so small. Having a way to combine them all into one collective storage in your house would make that much better.
On top of all of these there are just constantly new items being added to the game like motifs and such which also adds to our encumbrance.
My suggestions to fix these issues are to add a gear storage locker that is shared on your whole account basically the same thing as the crafting storage bag. This could be an ESO plus bonus. Also allowing us to purchase more storage for our bank and characters bags through crowns would be beneficial for players and ZoS. I rarely purchase anything from the crown store, only functional items like race changes and such so for people who don't care about cosmetics this would be another avenue for us to dump our crowns.
I don't really do any housing at all but we also desperately need a furniture bag with unlimited capacity. As it stands people just throw all of their furnishings in a trash house for long term storage which makes seeing what you have available just a massive pain I'd imagine.