It's what they were and are bred for and it's the way they move
The gaited horses are usually smooth and you don't bounce like you would on a trotting horse. I'm not sure HOW they got started with the gaits, but I can look it up for ya if you want. The Fox Trotters do a Running Walk and a Fox Trot, the Fox Trot is a diagonal gait where they walk in the front and trot in the back. It's smooth gait and their feet SLIDE into place rather then just hit the ground, it's when the feet HIT the ground that makes the ride so bouncey. Now they can do all of the normal gaits like trotting and cantering and galloping, the smooth gaits are just added in. You don't really want a gaited horse that trots, you want them to be smooth. I'm not sure how they move in the Running Walk...You should go look this up too, I'm no expert, I just know from exprience
I hope this helps!