I've heard two separate explanations for why 20 rep squats are only for legs and not for other body parts:
1) Human's legs have evolved to deal with "high reps" by their very nature (we are able to walk long distances, runs, etc.), which other body parts rarely do such "high rep" activities. Therefore, high reps are the appropriate/proper way to strain that muscle.
I'm not sure I really buy this explanation, because from that perspective 20 reps really isn't that much higher than 8 reps (example: from an evolutionary standpoint, we might lift 10 heavy things a day, but walk 2000 steps - therefore, this logic would seem to make more sense if we did 200 rep squats).
2) The benefit of 20 rep squats has little to do with the legs, and more to do with the hormonal reaction of a compound exercise at such extreme intensity.
This makes more sense to me, and would suggest that certain other compound exercises might also provide a similar benefit if performed in a careful enough manner to avoid injury. I suspect that there are very few exercises I could properly perform at a high intensity for 20 reps.
I would suggest experimenting with different rep ranges. For me, I've found that 4-8 reps is normally optimal, although the truth is, I have always found that intensity + proper diet + avoiding injury + compound exercises is really the key formula, and trumps some sort of magic rep range.