Neat picture and some good info in it.  Thank you!

It opens the pocket on the shoulder for placing the rifle butt, an old target shooter technique.

Rotating your elbow to horizontal and rotating forward a bit creates the pocket for your buttstock.  I think it helps follow up shots, and is a more secure platform. Less muscling to steady the weapon and I’d say more accurate. At CQB ranges it is a greater target.

If you wear body armor you can’t create a good pocket as your shoulder pocket is covered by the plate. I think it takes more muscle to hold the rifle in place as you have the inner edge of the buttstock, not the whole surface, against the plate.  Those are good reasons to square against the target; many say it’s plates front toward enemy but it’s also getting a better contact of the buttstock to your body.

I’m not a subject matter expert but that’s what worked for me.

Yes. There are pine trees on Pacific Islands.

The weapons of the day (03 Springfield/M1 Garand/M14) also fired full power cartridges that would be pretty stout for recoil. Creating the pocket helped control the guns . Especially when in the standing position, which was in vogue back when basic marksmanship was taught.

Intermediate cartridges are much easier to control, combine with body armor/plates made the need/practicality of the pocket less.

I use the chickening/Pocket when competing /shooting Service rifle. When I'm practicing with my fighting AR, I do not.

I liken it to being able/knowing how to use a sling... I don't need to often, but when I need to, it's a nice tool in the tool box.

Back in the 1990's, I bought a brand new S.A. M1A that came with a lockbar rear sight.

I sold it later to fund a USPSA/IPSC pistol

can't find a better pic than this