I don't want more space. I want better space.
Up to this point the storage we've been given is just a large empty room with a couple of specialized areas. But specialized containers in real life help organize our stuff. And the parallels exist in game storage, too. Different storage systems can present their information and have specialized user interfaces in ways that make their contents more useful. Again, in real like or in game.
People who came in late like me might have a lot of started, but unfinished projects -- e.g., relics, tribe tokens, chocobo registries, Bozja upgrades, etc. I can tell you I have a ton of stuff that's partially complete and it takes up more than two retainers just for that. This isn't just hoarding things with no use, but things that I'm actively working towards. But given that you can start things way faster than you can complete them, they can accrue. And one of the main reasons to start multiple things is so that you can progress on multiple things with the same task. Right now, I'm progressing relics and Yo'kai weapons at the same time. And being efficient with task time is kind of necessary when you came in at the end of ShB and not the beginning of ARR.
A specialized glamour dresser storage could show you that piece on your character alone or as you already have. We have this functionality, but I have to be curious about the piece to see it on me. Why? Eorzea Collection does this well. A tacklebox could include information about what fish they can catch plus potentially other information that we have to look up. We already have multiple specialized storage options. Anything that's miscellaneous registry like minions, mounts, and hairstyles have specialized storage. I think all the places where we already have specialized storage have been big improvements over the general storage they could have had. Imagine if you had to reserve space for specific mounts in your general inventory. You could say that you could key bind individual ones, but specialized storage here is much, much better.
I think the things that people keep asking for specialized storage for are in desperate need of improved UI and addition context.
Glamour items could be presented better and include where to get them. They could have previews and a "book" showing multiple options at a time would be great. Again, see Eorzea Collection. Glamour storage would also solve the problem of needing replicas.
Crafting Materials just need better management and presentation overall. I would love to put them all in the same place rather than across retainers. I would love to be able to identify what stuff is normal material and what is *, **, ***, etc. I would love to be able to filter by expansion.
I think there's plenty of interesting things that they could do that would remove friction. Dealing with these things isn't difficult -- it's tedious.