They actually do. You’d have to know about biomechanics to understand why, but it’s roughly summarized as: legs have more muscle (as a general rule) but a very limited range of motion. Often when falling, you have more than just downwards momentum acting upon you, so the muscles in the legs are often underutilized. Arms, on the other hand, can use pretty much all of the muscle groups in the upper body at once and in any direction. It’s why our first instinct when falling isn’t to outstretch our legs, but our arms!
Anyway, as promised. Shorter fall, but same flat damage.

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