Which would then support my original feeling that unification is not necessarily the road to take here.
Well, I could not disagree more, but you already know it
Not only there's no unification between different building categories (workshops/constructions/rooms) in your version, there's even no unification inside what a perceive as a single category (bedrooms, hospitals, etc.). Which is IMHO very bad.
And please note what I've written about having bedrooms, barracks, etc. in the Building menus. I feel it's very crucial to have them there.
It seems that it just makes sense to remove stockpile designation and just have zones that can act like storage.
Well... stockpiles and zones are just two names for the same thing. Even now they work basically the same way. You draw a rectangle and then set its properties. So yeah.
But I'd say zones should be removed completely. Part of them is rooms (hospital, meeting area), part of them is stockpiles (garbage dump) and part of them is designations - or "work area" how I call it (fishing zones). There's no need to have them as a separate building type.
EDIT: When I say "remove zones", I mean remove them as a separate option in the menu, not remove the principle. As I've said, I like how hospitals work, for example, and would extend it to other rooms as well.