More to the point, I do not want some algorithm "helpfully" sorting my incoming email into different views according to some opaque criteria that I don't get to define or tweak: I want to see everything in my default inbox, no exceptions.
Permitting someone else to sort my mail via rules I have not defined is how important business email gets missed or overlooked.
Exactly this. When I saw the tabbed inbox, my first thought was, "oh, this will be cool", followed shortly by, "wait, I don't get to control or customize this at all?"
Really, why can't I define my own tabs for specific searches/labels? The black box tabs they provide now should just have been defaults within a customizable feature.
Personally I think it's a great feature but one I won't be using because I already have a labyrinth of filter rules that perform the same function.