I may be wrong but I sense that this question is submitted with a bit of attitude attached. My very short answer is some of my riders go showing alone. Some only go when they have help, either coaching, grooming, videoing, or hand holding. And some play it both ways. In the long run I cultivate their independence, and I’m proud when I’m doing a weekend clinic to be receiving texts and scores from my people around the country.
However, I am also totally comfortable with coaching riders who aren’t yet ready to leave the nest. If handing them a water bottle, reminding them to pull their wraps, or to drop the whip before the Championships lets them focus better on the job at hand, that’s all fine with me. I don’t think instilling good habits in them fosters a permanent dependency.
If you are feeling knowledgeable, strong-willed, and independent (or impoverished), I have no problem if you want to go it alone. However, even Olympians use educated eyes on the ground when they can. To an FEI trainer Intro B or Second Level One may seem impossibly mundane. For a child or a middle aged novice sometimes simply riding in public can be highly unnerving. If you can’t empathize with the swirling stew of emotions that may be clouding your pupil’s mind when she goes off to compete, you just might be in the wrong profession (or at least teaching the wrong people)!
As for what goes on in the warm up arena, I too overhear a lot of useless drivel but it doesn’t have to be that way! Aside from just plain bad advice, sometimes I hear what sounds like an actual lesson happening, at times more to impress the spectators than help the student. And ten minutes before your ride time is a bad time to rebuild your seat or change your system of aids. Good coaching is minimalist. I endorse that old line: “Don’t tell them everything you know. Tell them what they need to know at that moment!” Good coaching is also very individualized. The trainer has to know whether to pump more intensity into his charges or to bleed some off and help them relax. It’s all about trust—initially offering trustworthy advice, eventually helping the riders learn to trust themselves.