No idea actually; not really my scene I'm afraid but can't imagine it would really 'work' with showjumping other than if you were just doing fittening canter work. We used it in NZ on a couple of polo ponies when doing sets (riding one, leading two) going round and round the polo field at a gentle canter to save their backs if they were especially bouncy. Polo saddles are not very comfortable and rising canter can help get a nice rhythm on a big or choppy striding horse. Someone else can probably explain better than me!
I am not sure how much it is a training technique for the horse, but showjumpers and eventers use the technique quite a lot for improving their own sense of rhythm on a particular horse, because the physical motion of rising for one canter stride and then sitting for one canter stride helps you focus on the tick, tock, tick, tock rhythm.
It's what the sj'ers do, when they look like they're sort of not able to sit a canter..lol.. Watch one of the top sj'ers on utube. I don't know the reason for it though..
Just read the above replies, now I know the reason lol
I do this quite a lot, its easier than sitting when you have a bouncy horse, and I have a bad knee so it's easier on that too. Oddly I sit to her trot - as she's so smooth, and rise to the canter... (mostly all to do with kneeache!!) Agree with OP, gives you a real sense of the stride, quite hypnotic really