I was watching a video recently from the African hunters school which advocated dropping the stock down for a reload. 2 reasons. 1) it gives you a much greater field of vision and also lets you see in the corner of your vision that the empty is out and new one is in, and 2) it makes you remount and aim in one flowing motion - just like a shotgun.

I can absolutely see the logic - with a shotgun I Shoot as but hits shoulder and would do the same with a rifle on a quick shot.

Reloading in shoulder might be quick, but does it get an accurate shot. Saying that I shoot the old English style with barrel up and tip of barrel into line of site onto target and then lift butt. I have military friends who keep butt in shoulder and then lift rifle to the target. They shoot shotguns the same way.