I have a feeling that has more to do with the fact that as a braider it’s easier to stand on the “correct” side (i.e. the side you ALWAYS stand on to braid) and pull over a left-lying mane than it is to stand on the “wrong” side and try to braid in the opposite direction.
And I couldn’t provide an example, NOT because no one does it, but because it’s such a minute detail when done well that I doubt anyone would notice unless it was pointed out to them. I do know a couple of horses who show in the hunters with roached manes, and same story…unless someone pointed it out to you, you would never notice.
These are the kinds of details that so many people think are important, but really aren’t.
Also, someone with a better memory (or more time to google) can probably tell this more accurately than me. But wasn’t the conventional way to braid, to braid on the right for stallions and geldings and on the left for mares (or vice versa)? I thought the side the braids went on was supposed to be telling, and we just kind of blew by that in the hunter world because it was more difficult to do??