I'm extremely uncomfortable with the idea of watching being outright "banned" (i.e. for reasons other than practicality, general space limitations). There is no reason, in fact I believe it should be actively avoided, that extensive time be spent alone during workouts with any kids, without other adults around.
I don't really think it compares to a classroom setting. There are other adults who aren't currently teaching wandering all over schools. Actually the school system I recently graduated from, the teachers aren't supposed to close doors as a general rule - it must be opened at least a crack, and even that degree is discouraged - generally they want the doors open enough to see into, even with high schoolers.
Some gyms just don't have that many other adults in the gym during team workout. Also, I'm just going to throw this out there, having done gymnastics myself, more negative experiences in a competitive gymnastics setting than in a public school classroom. Obviously there are a lot of variables there. I'm saying I wouldn't leave any child I was responsible for at a gym that wasn't just trying to get me to see practically why constant watching is not a good idea (I am so 3000000% in agreement with that) but told me I could not supervise that child. Nope. Not okay with that. It is certainly not unheard of in the US, but it's "not standard" enough that I'd go find another gym that let me watch. Probably wouldn't even work at a gym with such a rule. I can't offhand think of any gyms in my state where watching is completely banned anyway.
People who are causing disruptions should be dealt with. I think banning everyone is draconian though. There is a significant minority of people who need to be dealt with, but honestly I do not think the situation really warrants some kind of covert CIA nonsense. This is gymnastics, not special operations training. Of course parents can watch.
Also, I know people will say in other activities, like ballet, no watching. This seems to be true, but I'm just going to say, one of my worst experiences with activities, when I was a very little kid, doing ballet in some windowless room with a mean teacher who would turn out the lights to complete darkness when she deemed the preschoolers unruly, yelled, etc, once ended class right in the middle and stormed out. Not a great experience.