guns

it might have just been inherited from the Thompson, which these guns were apparently derived from

As for why the Thompson had it - part of it was probably just it being an early submachine gun and people still working on figuring out how to actually properly design them. You kind of need that drop in the stock for your face to line up properly with the sights:

Of course, if you simply had the sights higher up you could have a straighter stock - but at this point, infantry doctrine still heavily emphasized fighting from a prone position, and so having sights be positioned lower so you didn't have to stick your head out too much was considered very important. This reasoning is why we also see so many guns from this period with side and top magazines - too long of a magazine on the bottom would interfere with sticking close to the ground. The BAR was only issued with 20-round magazines, despite higher-capacity magazines existing and other LMGs of the period like the Bren & DP-28 having higher capacities, likely because those would just be too long to comfortably use with the intended doctrine.

Aside from all that however, I think it may have also had something to do with tucking the gun under your arm. While these days we generally dismiss the notion of shooting without sights, at the time this was actually practiced in certain contexts - there was even a fancy term for it, "point shooting" (although that seems to refer to more specifically fast-draw techniques, where the idea was to just shoot as quickly as possible in self-defense scenarios, while in the military context shooting from the hip might be more so related to laying down fire while advancing, which is instead referred to as "walking/marching fire")