I thought of one reason to layer, at least at the bottom of the pile.
It might be smart to put down a double-thick layer of browns on the very bottom of the heap, especially if you don't mix and have enough rain that some of the "goodies" sometimes leach out. An extra layer of browns at the bottom will absorb the "drippings" and capture the N that might otherwise have left the pile and gone into the ground under it.
Also, browns on the side help keep moisture in the center. Browns on top might help shed excess rain.
This kind of assumes that you have more browns available than greens.
Personally, "turning the heap" is almost my favorite garden task. Cultivating the soil is #1.
