So, is there any potential we could have LS-banks.

A bank shared with the community of your LS? Ideally you could restrict items to stackholders vs pearls.

I don't even mean the ability to deposit gil, though that would be fun. But it would be nice to, for instance, drop broken stacks of useful items into the bank. I just had to buy 99 baits to catch my guild fish. I've now got a stack for 89.

The nice thing about this is that it wouldn't "further increase zoning times" because it wouldn't have to load upon each zone. Guild banks could only be accessible from talking to an NPC, or better yet, talking to your moogle. Dependent on the linkshell equipped is the guildbank you had access to.