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Well CaptainMal It sounds like a good argument to me. But don't we put your heads down and apply cheek press with iron sights too.I have three model 336's with see-through mounts. Two of them also have peep sights you can use through the mounts. I seek them out to use because they work so well.
Every time I shoulder a rifle, I keep my head still. No crunching down to see into a low scope. Head straight with a minimum of cheek pressure. Cheek pressure is a BAD thing. Pulse and muscle movement in the cheek adversely affects how steady you can hold a rifle. Different cheek pressures can affect the impact point of shots by altering the recoil pattern and affect barrel vibration. Any change in pressures during a shot is a bad thing. Cheek pressure, unless tightly controlled, is a bad thing.
Now the rifles we are talking about are not precise shooting rifles. For how most use them and expect them to perform, any reasonable 2 MOA group is often considered excellent. Press tightly with your cheek and lower your head to shoot. That can move your impact points around and open up your grouping. Do it and leave more deer there for me.