Half a century ago, learning to ask a horse to canter on the right lead in continental Europe, we were to use the inside heel to ask, the outside leg to support the hind end.
That was because when you ask with your heel that inside leg is what starts the canter depart properly, from behind.
We didn't have problems with horses rushing into the canter, cross cantering or taking the wrong lead, even the first time we asked a colt to canter under saddle, because what that does, when you poke a horse right there, is a neurological response that brings that hind leg forward.
Once in the USA, many were asking for the canter with the outside leg, took me a while to catch on to that.
Doing that also had horses rushing into the changes and cross cantering and missing the proper lead part of the time.
There are whole chapters in hunter books about that, how to do it and how to work to correct bad canter departs, like the one by Ann Kursinsky, if I remember well.
I still will start canter the way I learned, with the inside leg driving, but then taught horses both ways, so it could respond no matter who was riding it.
Try it on yourself, have someone poke you on your side about your hip and your body will tend to bend a little and that side's hip will move forward.
I expect in a way some of that response, to bring the hind end under themselves, may be what is happening with the spur use, in many ways, including the spur stop.
Fine spur use is also what teaches a horse to move off your leg, once well trained and so facilitate lateral movements along with using that hind leg more.
We can train horses to respond any way we want them to, with any cues, installing any buttons as we can imagine may work for what we want.
The trouble with that, when we don't have a standard, you need educated riders that can keep trying buttons to figure how a horse was taught.
Those stiff, poking along wp riders look so ineffective up there, like they are not doing anything, but in reality, the rest of us that don't know that much about it, if given one of those very finely trained wp horses to ride, we would have a big surprise trying to get them to perform like they do without confusing them, just as those riders would be struggling with horses of other disciplines, if they were not aware of how to ride those and tried to get other than those spur trained horses to respond to them.
Our riding instructor when I was a kid, when we did something that didn't make sense, used to say "that is like asking a horse you are riding to back pulling from it's tail".
Once I did just that, taught this little mare to back when I pulled from her tail, from behind her.
He rolled his eyes at me.
We really can teach a horse anything, our imagination the limit.