I do think the danger is that people misuse the whips, sticks or ropes and chase horses or threaten them. This is common in some forms of liberty training that use negative reinforcement.
Whips and ropes and even people can become conditioned aversive stimuli, so just the presence of the tool or person affects how the horse reacts.
I used to carry a dressage whip when riding my mare, I never touched her with it but she knew it was there (previous training had taught her how to avoid the whip). Do we really want to train using avoidance? Or do we want a partnership with the horse, horses can become excellent puzzle solvers once we give them a choice.
So for me (and it is a personal choice) I only use a stick occasionally as a target to form certain behaviours. Once on a cue we can fade out the target and use a variable schedule of reinforcement, and a variety of reinforcers - these may be scratches, food or even a favourite behaviour.
Horses do like to play, as long as we can keep them under their emotional thresholds. Too much activation of the SEEKING system can also cause distress, just as activation of the FEAR (flight response) system can.
If we use aversive stimuli to train then horses can become very vigilant as they work out how to avoid the whip, stick or rope. This hypervigilance is exhausting and often we see very animated horses with liberty trainers and as soon as the trainer stops the horses seem to go to sleep, people then mistake this for a happy relaxed horse. We must be careful to watch the horses emotional state in all training.
Negative reinforcement isn’t necessarily a bad thing, if used sparingly and correctly. However we must be aware of how and why any reinforcement works and how it affects the horse.
Positive reinforcement stimulates the cognitive area of the brain, whereas negative reinforcement stimulates the flight/fight response especially in situations where the horse is driven away or chased with a whip.