I think it helps with rigidity once the box is made up. The two smaller end flaps fit inside the box and stop it warping. The outer flaps also do the same so combined make a very rigid closure.
It also forms a better seal to help prevent the contents falling out plus having the crease helps keeps the side of the box from bowing.
Try it, get a box and cut off a pair of flaps, making sure you also remove the crease. The sides without the flaps will distort easier and also the box will twist into a parallelogram with little effort.
First of all, let’s look at cost effectiveness. If you were to cut across one edge of the box and lay the whole thing flat, you’ll notice that all the flaps cause it to fill out a large rectangle. Getting rid of the shorter flaps wouldn’t save material unless you were making very specific size boxes to take advantage of the available space when tiling your cuts.
Now as for their usefulness, the smaller flaps help distribute the load of anything placed on top of the box across the whole width. This is especially important in shipping, since boxes will be stacked on top of each other in whatever shipping vessel you’re using. Without the extra flaps, the larger flaps would just buckle inwards when there was enough weight on top.
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