It seems to me that the main purpose of cutouts is that of combining a very wide tail and its huge leverage over the fin, with good longitudinal pitch stability. In fact reduction of planing surface at the tail should force the board use more forward surface to glide on, therefore obtaining a longer planing surface with more resistance to pitch variations. A no-cutouts "full width" planing surface would be shorter and therefore be more prone to pitch variations, somewhat like the board was hinged on the very tail.
On the other hand, probably a calmer water surface that one may encounter at lower wind speeds would make it possible to use the superior efficiency of a superwide supershort planing surface.
Thin cutouts IMHO are used to obtain gradual transition from a "full width" sub-planing surface to a narrower surface at speed.
Air pipes are to me a deep mistery, explanable only in terms of marketing bells and whistles. The side of cutouts has plenty of surface for the air to pass through and fill the void, if any, left under the board by the cutouts. I observe that in the case of F2 boards the cutouts are triangular, therefore air is shielded from getting directly under the board from the sides. I see that after 2 (?) seasons other board makers than F2 do not copy/use them.