Humans are slower than horses. When someone is working a horse from the ground using a curb bit (so called Kandarehandarbeit), sometimes the horse learns to move slowly and without any expression.
You can find clips of many people working horses from the ground, where the horses are barely moving. This is wrong and very dangerous, as the horses learn quickly to move in a very unnatural way. The haunches literally disunite from the front of the horse. Piaffer is not about making sleepy steps at place, but should be a very energetic movement in extreme collection directed forward.
It is very important to maintain energetic movements of your horse.
The ground work is a very good occasion to ADD THE ENERGY to your horse’s movements.
If you want to walk beside your horse at all times, you won’t achieve it.
You need to give your horse space, and many times you will have to run, and trot yourself beside your horse. You can do it at liberty, or with a light rope. You can also achieve this on a curb bit or a snaffle (Kandarehandarbeit) but you need to place your hand on the withers of the horse to maintain the position of the hand in relation to the horse’s mouth, even when the horse is moving very energetic. This is the only way to avoid pulling and restricting your horse’s movements.
Whatever you do, don’t make your horse stop moving like a horse.