That's mainly a practice thing, you have to practice claw to do it well.
Also kinda off topic but I actually claw in some games on Wii U, which is kinda funny.
Also my friend double claws on PS4.
Ya I tried for a good while in Halo 2, spent days running Midship FFA trying to condition myself to Claw, and outside of the benefits of executing buttom combos a bit better, my shot was a lot worse. It wasn't worth the dip in accuracy and discomfort after hours of gripping the controller that way, so I just went back to normal grip with some claw action here and there.
It's not for everyone, but there are some definite benefits to it, although plenty of high profile Pro's never really bothered to claw, or they use it sparingly like myself. So it's all preference.
As for Pro Halo Player Enable, this always amazed me about him.