lighting – Why don’t all barndoors have triangles attached to their sides?

I never used barndoors in a studio, and I’m not sure to understand how they work.

There seems to be two variants of barndoors. The first type, which is the most popular one, is a frame with four fixed-size plates fixed on it:

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The second type, much less frequent, contains a frame, two fixed-size plates, and two plates with triangles attached to them on each side, meaning that they can be adjusted depending on the position of the two other plates:

enter image description here

I was imagining, actually, that all but the cheapest barndoors would have four planes, and each plane would have two triangles that could be expanded or collapsed depending on the perpendicular planes. This would ensure the light will go only in the needed direction, instead of passing through the holes between the doors.

Where is my mistake?