Why do some cheekpieces have this notch?

While I am right handed, I am strongly left eyed and will often shoot my right handed rifles from the port side. There have also been a few occasions where a shot from my left shoulder made for a more stable shooting position. With or without a cheek piece, that clearance is functional and welcome.

My last black eye came when my new M1 taught me to change my grip on that rifle. I would enjoy greater thumb clearance there!;)
 
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