I'm not proposing that the current inbox go away; I'm proposing this as an additional view to it. So while you would have to use the navbar to use this new feature, you'd lose nothing.

(This is not an objection to having it be outside the navbar; it just struck me as the most reasonable - and least-cost - place in the current structure. Personally, I use the navbar, despite it being pretty unattractive. I've been wanting to figure out whether it could be customised. That would be nice.)