A large, buildable container, at least 8x8 big. Only one per town. Buildable only by town mayor.
And the fun part...
It can be accessed by any town member (with required priviledges) from anywhere on town claim through adventure menu, without having to physically interacting with the building. Of course it can still be accessed in normal way too.
Yes, it is totally unrealistic and so on, but I think it would be nice "quality of life" thing. We could have 2 different versions - smaller, and a bigger one, which would require some cash shop stuff.
Example 1.
Another town member needs an item I have in my inventory. Instead of walking to him I just put the item in public vault and he takes it out
Example 2.
I want to coal / lime my fields. Like, massively. However, my grinders / coal piles are far away from the fields. Instead of walking between fields and coal piles, or loading coal / lime on cart, I just load it into public vault, walk to the fields, take the coal / lime from public vault and drop on fields
Example 3.
I'm foraging. Instead of having to walk through the gates everytime my inventory is full to unload the stuff I gathered I simply enter town claim and drop the stuff in public vault. When I'm done foraging I return to the village and sort the stuff and put it into proper containers
Example 4.
I'm cooking stuff that requires multiple different reagents. Instead of walking from a container to container, cooking 3-4 items and repeating I simply load all the reagents into public vault, go to stove / baking table and start cooking while taking reagents from the public vault on the go