The muzzle must be kept low, the swivel must not damage the fore-end hand, the sling must not pull on the barrel or the stock and there must be a place to mount the bi-pod without changing point of impact.
All this is solved when the rifle is carried butt up and the front swivel stud is mounted on the front action screw or on the stock just in front of the bottom metal.
Carrying the rifle on the left shoulder with the muzzle forwards and down (for right handers), with the left hand on the fore-end, controlling the muzzle direction, allows the right hand to be free. It is faster to shoulder the rifle from there as well. In the photo above, picture the man with the AK carrying it over the left shoulder, upside down. Then figure the time and the moves to get shooting compared to the man with the double, regardless of on which shoulder the double is carried.
Carrying the rifle muzzle down also prevents water or dirt from falling down the bore and, mounting a bipod just ahead of the action or on the front action screw, makes a bipod more versatile.