I’m not the first to point it out, of course, but so much of this has to do with the job any given horse has to do, right? (I’m in the H/J world.) To take the example of moving off while being mounted - a beginner lesson horse doesn’t do it because part of the job is taking care of beginners. An international performer does not need to take care of beginners - they need to win, and there are a lot of other things to stay on top of regarding training and fitness and mental management that are a lot more “important” than standing while mounting. I was specifically taught the skill of mounting a new/unknown horse expecting it to move off, and often requesting the horse to move off, because you don’t know which ones are cold backed, and it’s a different rider safety issue than a beginner lesson horse not moving off without its beginner rider.
Perhaps a way of explaining why one stereotypical culture is different than another stereotypical culture is that the respective markets simply don’t demand or value the same things. If every arena-specific discipline demanded that the same skills be installed as every open-range discipline, they would be. But the markets prioritize differently. Different philosophies, preferences, or holdovers from an earlier eta, not objective requirements. It’s simply not necessary for every horse in the world to tie to the side of the trailer when standing on the trailer instead works for their job. It’s a convenience, not a requirement, for many disciplines.
Don’t make the mistake of conflating dangerous bad behavior such as biting, kicking, or rearing with annoying behavior such as walking a step behind the handler or pinning their ears when grooming the girth area. I was a pro H/J show groom and can honestly say that it did not matter if the fancy 3’6" hunter walked a step behind my shoulder coming in from turnout. They weren’t dragging behind, they weren’t stepping on my heels, they just. . . walked a step behind. But any dangerous behavior made a horse harder to sell (to the vast majority of the market) as well as being a safety issue for workers and clients, and it was addressed as such.
Also don’t make the mistake of conflating the elite 1% of the international competition horses like those profiled in COTH (an English-focused publication) with the vast majority of professional and amateur programs out there. They are not representative of anything but themselves, and they are in a rarefied and high-level world. If they were truly a danger to those who own or handle them, it would be addressed. Otherwise, not the priority.