THESE ARE NOT MY VIDEOS.
Above's a video of a Dunit horse and its head carriage. Note the stops at 1:30, 3:39, and 3:50. Since his head is low, he is more balanced at the end of the stop to catch his balance for the next move, either a reverse or turn.
Here's a Peppy Badger Chex prospect, and from :59- 1:10 even without a rider, you can see his natural head carriage is low.
And this, a Spark horse, (one with that high neck-set) and if you watch his stops and spins, beit they are GORGEOUS, watch how much his poor head bobs when he lowers his head to stop and spin, and how hard he has to work to get the rollback. Which isn't that great, because of the way he stops.
Now, after seeing that spark horse there, take a look at this Wimpy bred 4 yr old. I had to watch this whole video a dozen times over. The only thing I could even TRY to criticize was the first rollback at 2:30, he threw his head up when he turned around, and he's young, so he swished his tail and pooped...
Here's a cutting horse with a lower neck-set, you can see immediately, even before the horse gets a cow. Then look at him as he moves toward the cow at 1:10, and 1:14, BOOM, that head is DOWN.
It is just easier for the horse to continue his momentum if he naturally puts his head down. Think about it this way: if a horse stops with his head up and has to yank back to the other direction, he either has to drop his head and his front end and throw himself the other way, or he has to rear up on his hind end. But, if his head were down in the stop and he had to go back the other way, he's already down, so he can save the time/energy and have the momentum already going for him.