yup. That's why I always say (and was always taught) you don't get better canter by doing more canter. You get a better canter by doing more trot. I've found that 90% (ok maybe not quite that much but roll with me here haha) of balance, muscling, stiffness, and rushing issues and even many chiro issues can be fixed with a solid trot regiment of conditioning, bending, and changing diagonal (ever few strides while going in the same direction to make the horse use their hind end evenly).
Try it sometime - even on a school horse though I know you can't do the full conditioning. But try when going around the arena changing your posting diagonal every 3-6 strides or so without changing direction. A stiff horse will brace that change, pin ears, tense shoulders/neck/back. A looser more balanced horse will not change gait or stride or rhythm at all. My clyde cross couldn't care less. My hot ottb who tends to be stiff to the left starts off pissy then relaxes as he loosens.
It's a GREAT indicator of how lose, balanced, fit, and evenly muscled your horse is. And if you tend to favor one side more than the other also. It's also a great workout to help loosen a tense/cold backed horse esp in winter!