Demonstration of the fact that binning actually reduces highlight headroom.
A pure 0-255 gradient was made, then noise was applied, image was divided into 4 strips, from top to bottom:
Original Pixels
Pixels Binned 2x2
Pixels Binned 3x3
Pixels Binned 4x4
Then the image was clipped at 205.
The original, with its higher pixel-level noise, actually has more headroom.