"If you note, whilst curved, there's not much drop between the axis of the bore and the tip of the buttstock."
That's why I believe the extreme curve itself of the Afghan Jazail was designed more for carrying the gun versus shooting. While every example I've seen has at least a provision for a sling, It's my belief that the curve was for carrying the gun under the arm pit while trekking when it was desired the gun be in a "ready" position. Whether on foot or horseback. My reasoning for this is that if you look at the butt stock, it is overly thick at the wrist area. But then the THICKNESS of the butt stock thins dramatically towards the butt cap. If you hold the gun under your arm pit and walk with it, it is a very comfortable carry. That's why I think the butt stock is thin and flat going backwards.
This would be useful while trekking in the mountainous regions, especially since the barrels on these Jazails tend to be long and heavy.
Additionally, as Cutfinger mentions, many of these Jazails had rudimentary type peep sights at the rear of the breech, often forged with the breech plug itself. This tells me these guns were made for longer range shooting, from a rest. Even if the rest was just the rocks on a mountain. Some of these jazails were even made with an integral stand made of wood, iron, and leather.
Again, I've never seen any documentation for the reason for the curve in the butt stock. So I, like others can only speculate. But to me, the curve being used primarily for carry is the most logical I can come up with.
Here are some pics of my Jazail shooter. Notice how thin/flat the butt stock becomes from the wrist area back to the butt cap.
Rick