You are absolutely right, Patti.
While many gaited horses have a high head set it is certainly NOT universal. Further, the higher the head the more ventroflexed the back and instead of the back end (where the real power is) pushing
the horse the front end is "pulling" it. The ultimate example of this the TWH Performance Horse. But you'll see this in the Walking, Racking, and Spotted Show Ring. That's because in those venues "front end action" is what wins ribbons. Anywhere else in the Whole World a horse that converts calories into vertical motion, vice horizontal motion, would be considered "defective."
You have the right idea. Good luck as you move on!!!