Interesting idea, but any internally toothed washer I've seen doesn't touch the thread of the screw it's on.
It is true though that the bottom surface of a nut generally bulges slightly, so it's contact patch is circular or annular and slightly further from the threads the nut is put onto than an equivalent bolt's contact patch would be. The pressure distribution under the head of a bolt compared to under a nut is probably slightly different too.
Specifying the washer so the teeth line up with this contact patch could lead to externally toothed washers being used under nuts and internally toothed washers used under bolts. Never really thought about it before though.