There is a HUGE difference between using a whip or crop and using long, split reins to DEMAND a horse go forward.
It is not unusual for horses to learn when the rider has a whip. This is also true for horses on the ground, too. They learn to ride and behave differently when their handler / rider has that whip in hand. They literally learn to respect (or fear) the whip but have not learned any respect for the person. I cannot count the number of times I have watched horses ride differently with a rider with or without a whip.
The other problem I see is that most riders carry a whip in the same hand all of the time. Their horses quickly learn to 'duck around' and do a 180 away from the whip any time it is raised up or used for more than a 'tap'. They also get accustomed to not responding quickly to the leg but respond to the visual 'cue' or 'aid' of the raised whip. That is NOT a legitimate cue or aid.
The difference of using the long, heavy reins is that they do not rest in the rider's right hand like a 'cocked gun'. They just are there all of the time. The other big difference is that when you learn to use an ' over and under' type of spanking action, the horse does not duck around but goes forward quickly. The 'front door' is the only one open to the horse and about any horse will get their butt through the door immediately.
If you do not think this is true, just look at how many horses spin around rather than cross water when their riders try to use a crop or whip. Reins work nearly every time to get the desired response while using a whip just usually teaches a horse to duck around and go the other direction.
Obviously, there are steps that are necessary for the rider to take when they use the end of the reins for discipline.
First, make sure you are NOT holding the reins too tightly by pulling on the horse's mouth at the same time. You MUST leave that front door open. We only use 7 1/2 to 8 foot heavy weight harness leather reins. They are long enough to let you do this (but that is not the main reason we use them). They have enough 'feel' to them that just moving your hand a little (with slack in the reins) gives a horse a pre-signal of impending action. Well trained horses will respond to just the moving hand with the reins still slack.
Second, if a rider has to use the reins to spank a horse, then, as soon as the horse has gone on and done the right thing, the rider should repeatedly pick up the reins and swing them around so the horse does not think that every time the rider picks up the reins, a spanking is coming. We do this all of the time on every horse -- not just after a spanking.
Most importantly -- if a rider needs to spank a horse, do it hard -- never using little 'taps' or 'slaps' with those reins. Do it hard and it will be effective. If you have to spank a horse more than two or three times -- EVER -- to get forward impulsion, you just used the reins to nag and peck at the horse. You usually get a completely opposite response. The horse will get MORE obstinate and will have LESS respect for the rider's requests. If you are not prepared to spank one hard, don't bother doing it at all.