Well, pivot grabs are good for covering options behind you. In an m2k chaingrab he uses pivots to always turn around when he needs to, which makes turning in place very useful.
Another example I have is when I play Marth and want to punish someone who mindlessly approaches. You can just dash back and shield pivot (there are a couple different kinds) and use his long grab range. Pivoting is good because it lets you turn on a dime when possible and executed right.
Why are pivot grabs different from JC grabs? it's because you have to dash one way and back to do it. In a dashdance, there is a frame where you are in your standing animation. This means a grab preformed on that stage is going to be a standing grab. You could always dash forward - back - then JC a grab, but that takes more time, and you would most likely be dropping a combo. JC grabs are better used when approaching.
Hope that answers your question!