Many people want a shorter LOP because of the way they learned to bring a butt stock to the shoulder. They try to bring the butt up as straight to the shoulder as possible, kind of sliding it up the shoulder, thinking this is faster and/or more efficient. That not totally wrong, but while learning, many tend to hit the armpit on the way up. They eventually master it, but at the expense of a 12 1/2 to 14" pull, instead of the 13 1/2 to 15" most adults should be at.
I learned this same way, and it cost me many a pheasant and duck, when I'd try to shoulder it the same way I did in the spring and summer on a t shirt in the field on October wearing a shirt, sweater, and heavy coat.
When I started getting serious about Trap, my coach showed me how he mounted a shotgun (and rifle, for that matter). Push the gun out at arm's height, pull it back into the pocket of the shoulder, and place the cheek on the stock, wood on wood, as he called it. You shouldn't have to move the head down much, and ideally not at all to do this.
He had me do it 100 times in front of him until he was satisfied I was doing it right, then had me do it with my eyes closed, then open them after the gun was mounted. The view should be the same as when done with eyes open.
You're thinking, " OK this works great for Trap where you have all the time in the world to mount the gun, but what about hunting?" Once you are proficient with getting the mount correct slower at first, speed up the practice until you're satisfied with the speed. I shot a lot more of the ducks and pheasants I'd have missed had I not learned this.
It is one of the first things I teach when I coach Trap, right after testing them for eye dominance. To this day, I can throw an 870, 1100, or Model 12 to my shoulder very quickly and have it right where I need it to hit what I am shooting at.