None of the above explains schuetzen buttplates or modern target buttplate hooks. Ask anybody why those exist and the answer is not "style" or "loading". There is a legit technical reason, obvious and agreed upon by everyone. Extensions on the butt hold the butt down and the muzzle up. And this is especially true when the left hand hold is significantly aft of the rifle's balance point. The heel and toe of crescent plates are extended just like schuetzen plates for exactly the same reason. They support the muzzle of long or heavy barrels.
In Asia you see plaques next to toilets, diagramming for the locals that you sit on the toilet. There's a red slash showing that you do NOT climb atop the toilet and squat. Laugh all you want, but climbing on a toilet and squatting makes a h*ll of a lot more sense than mounting a long sharp crescent plate to the shoulder pocket.