Classical dressage is all about training the horse's body to support their fitness over time, something like pilates does for humans. Classical dressage moves are all things you might see a fit athletic and happy horse do spontaneously by themselves at play, just refined. And refined is the word, the training methods for classical dressage are all about supporting the horse and refining their movement in incremental stages over a long period of time as their fitness develops.
It still broadly serves this purpose and proves the all round trainability and versatility of a horse and the skill of their rider in the 3 day eventing (which has just been on this weekend).
The competition of pure dressage (yet to come in this olympics and is the sport that C. DJ has just been banned from) is a bit of a far cry from classical dressage and I do think has lost it's way.
What CDJ was filmed doing is wholly unacceptable and is not necessary for the sport. It wasn't even productive, as effectiveness as a training method goes it is also just pointless - it just made a horse scared and sore, it didn't improve their movement.
There are good and bad in any sport, and equestrian rightly comes under scrutiny as it involves animals. CDJ was famous in the horse world for being one of the good ones for horse welfare, which is why this revelation is even more shocking and disappointing to us.
From a horse welfare point of view jumping has it's unique problems and racing has more obvious ones, and it's are WAY more endemic and it churns through a much higher vote of horses.