Couple reasons. First, like you said it's 8 more damage. Damage is always damage, but for literally double the risk in having it broken, I'm not sure 8 damage is worth it (it actually feels like more than double as you can catch people with the tackle by surprise and the first part is rarely broken, whereas they have time to prepare for the second part of the arm break). You would think that damage scales on HiC, but nope. Still just +8 for some reason.
Another interesting thing is that the punch version causes a floor hit with the last strike, whereas the arm break doesn't. I know what you're thinking: "Oh, well than the +10 on an explosive floor would make the punches net more damage than the arm break!" But no. Unfortunately it only get's +1 damage, making it still 7 less than the arm break. However, with a breakable floor, you get the full +10 damage, technically giving you 2 more damage from the punches than the arm break, and setting you up for a nice follow-up floor grab on slow opponents.
Lastly, I just think that aesthetically punching my opponent in the face repeatedly before headbutting the crap out of them looks cooler than turning their arm into my personal dildo.
Overall, I just find the risk/reward a bit skewed to convince me to use the arm break, though I do use it on occasion. Now I know what you're gonna say: "But at round 3 on the bottom floor of Scramble, if you had done the arm break, you could've taken the match right there. Instead you gave him a chance to come back, and lucked out he messed up." And you are absolutely right. That was totally an instance where I should have used the arm break instead. Muscle memory got the best of me.