I have let the horse pick their gait and speed. I've bought a few show world and gaming rejects that seemed to be unsure when traveling normal, uneven ground. Once I knew they really did have stop, go, right and left in their repertoire, I let them travel at will. Sure, if a decision needed to be made, mine stuck. But, it did seem to help them relax quickly.
If I'm riding a long distance to check something, I will let a horse choose it's gait, too, if it's safe to go faster when they want or we aren't dealing with time constraints. I know when I allow this I may get some "I feel good" wiggles from them as we go.