I've always felt that correct canter departs are extremely important. They affect a rider's true understanding of inside leg to outside rein, but more than that, they develop the FEEL (feel is everything and the only thing) for balance, throughness, and self-carriage. Maybe it's the impulsion that a canter supplies that allows or helps some of the rider's aids to succeed. I think we've all tried to bend and soften and achieve movements at walk that don't really succeed because we can't generate enough impulsion. Many times instructors say to trot or canter to regain forward impulsion before attempting some new movement or concept again. Having said that, a correct depart is very different than just achieving the canter gait. It is not running into canter or falling over the inside shoulder into canter. I guess it's because most of us didn't come directly into dressage but came through other disciplines such as h/j or saddle seat or just trail riding. Those other disciplines (at least at low or beginner levels) teach cantering from outside rein and outside leg back (kicking). This causes the horse to sort of leg yield into the canter and fall over the inside shoulder. The unintended consequence of this is that the horse uses its neck as a lever (and comes above the aids) in order to help bring its forehand back up. Then the rider has the more difficult task (or at least added task) of "packaging" the horse in the canter after the depart for proper uphill balance and "jump" and throughness, softness, and collection. The reason some of this happens is that in "falling" over the inside shoulder, the outside hind is left out behind the horse. It should be under the horse supporting the first stride of the canter. It should be the "one" of the "one, two, three" of the canter stride. When we allow the horse to fall over the inside shoulder, we are really kind of coming in on "two" (inside hind, outside front) and falling further to inside front.
Please bear with me. I know I am long and wordy, but I so want riders to get this that I maybe explain or "draw pictures" too much. Anyway, riders develop this way of beginning their canter from their previous experience and body memory and, frankly, from riding a lot of young, green, or messed up horses (rather than the ideal schoolmaster) where just achieving a canter at all is a success. Might get by with this at low levels, but as we move up the levels, more quality is demanded. I always say "inside leg forward, outside leg back, shove with the inside seatbone forward, hold until the horse lifts into the canter, and release thru the inside rein". That's already a lot to think about, but what's missing is timing. I know this but don't say it enough. Often, too, I think the rider released or "dropped" the horse too early, when in reality, the rider asked when the horse's outside hind is on the way back instead of on the way forward. It's a feel that must be developed. Too much else suffers from this one little oversight: bad things like coming above the aids at the withers, falling on the forehand, losing the back, total loss of uphill balance which, in turn, causes contentious downward (non-existent?) (crappy?) transitions. In conclusion (Woohoo! Yay!), you can count on me stressing this timing more from now on:).