We do that at my camp. I completely agree with you that there are occasions that could make it very dangerous (I've been part of one myself) however, imo, it's more dangerous to get each little child on while their horse is loose since, at least my camp's horses, will wander off to kingdom come and completely ignore their riders. Since I only had four wranglers, myself included, to manage getting little kids on 10 horses, showing them how to control the horse if need be, then once the front and back wrangler got on, only two on the ground, if the horses were loose and wandering it would have been mayhem.
On top of that, some of our horses really hated each other and if they could they would attack each other. If they weren't tied up, they would think nothing of doing that with a child on their backs.
Each ride is a 15 minute slot so we have to basically throw kids at horses and get them on the trail or else the parents will start calling to complain. I could care less myself about complaining parents but the camp director cares and doesn't understand horses AT ALL so if I want to keep my job I need to get those kids on the trail. I would just not work there anymore, but those poor horses come from seriously misguided homes and I feel like I can do a little good towards making their summers be ok.
It's certainly not the best that it can be, but all the horses were well trained to tie (the one thing they were well trained to do! Hahaha!) and they soon learn that that's the way everyday goes and they couldn't care less. The only time I've ever seen a problem, in my 3 summers of working at this camp, was when a new horse who wasn't used to the system joined the system in the middle of the summer. She was already scary weird to begin with but we were giving her a second chance and she totally blew it. But in her case I think it had less to do with our tying thing and more to do with how she was bonkers.