It is important to use your hips in Karate, but we are taught that our power originates from the ground. If you aren't stable in your stances, if you're not grounded, your attacks and blocks will be weak. No amount of Shakira hip action is going to change that.
I realized that this is basically true in Jiu-Jitsu as well. How many times have we heard "You need to have a solid base". What is that base in relation to? The ground. "Get your hips under you". Why? So you are more stable, more grounded, you have more power. Your relationship with the ground is paramount in Jiu-Jitsu.
It even applies in ways that might not be as obvious. Even though my husband only outweighs me by about 30 pounds, when he gets me in knee-on-belly, it feels like an elephant is stepping on me. I told him so and he said "Well, when I do it I don't think about putting my knee on your belly, I think about putting my knee on the ground through your belly". Talk about grounded! Which is why I never ever let him put me in knee-on-belly anymore.This way of thinking is similar to what we hear in Karate "Don't punch your opponent, punch the wall through them". I suppose for Jiu-Jitsu it would be: don't lay on your opponent, lay on the mat through them. Pins work better when you are grounded, and the best way to ground yourself is to just relax and let gravity do the work.