I consider tying one up until he gets happy, relaxed and completely settles (this means his head is down and a hind leg is cocked) to be one of the most important aspects of a horse's training. I think it is so important that I will not even train on one until he is settled. When you try to train one in a less receptive frame of mind, you DO NOT have his mind, his cooperation or his concentration. You have a 'reactive' horse and not a 'receptive' horse. No 'good' learning takes place when a horse is reactive. He will get mad, get 'on the fight', be flighty, look for excuses to misbehave and will argue and fight you tooth and nail. You either have to exercise one until he is ready to drop (not good for minds or legs) or fight him until you win. I can have 3 or 4 productive training sessions with receptive horses in the same amount of time I can fight a reactive one.
I have found that once they have figured out that they are fighting themselves and not you and figure out that there is 'life after standing there', they take less and less time to settle down and actually start to try to learn. You can turn one out, tie it up a week later and in 5 or 10 minutes the horse will drop its head and rest a hind leg.
I used to do the exact same thing at a show or big horse gathering. I would find a 'practice roping' or a 'playday', ask the proprietor if I can bring a horse and tie it up for the evening in an 'out of the way' place. I used to tell them that I would flag for them or work the chute or warm up their second horse by loping circles for them or ???? if I could bring green horses and let them get used to all of the noise and activity. Again, it is so much better for the bottom line of training than trying to fight a reactive, or nervous horse. I have not had one that did not finally 'give it up' and rest.
With horses that I was seasoning and getting ready to haul, I had to get them used to both being tied up by all of the noise and activity and then had to tie them up well away from the activity so they would also learn to be happy with complete separation from all other horses.
Horses do not forget anything. I have taken broodmares that had been pretty well trained 5 or 6 years earlier and brought them back in to ride. When horses got so cheap, I quit breeding 3 or 4 of them and put them back to work as 'trail horses' for the commercial trail string we have. They whinnied and fussed when they were taken from the broodmare pasture, so I just tied them up until they settled down. [They had all gone through this when they were trained initially.] I took them out one at a time and I do not think any of them took more than an hour at most to just stand quietly. 'They knew the drill'.
The main thing we have found is that you get nothing done if you interact with the horse during this time. Each horse has to just figure it out for himself.
We trained a cutting horse mare for a man that had to quit hauling her because she went crazy when you tried to take her from her barn. She could not be ridden down tired enough so that she would not whinny or quit a cow right in the middle of a class. He tried hauling her neighbor horse with her and she still whinnied. We tied her out to an over-hanging tree limb about 150 yards from the barn. She carried on so bad that she made a hole about 10 feet across and about 3 feet deep. Husband had to fill the hole up twice the first day using a big tractor and front end loader. The second day he only had to fill it back up once. About noon on the third day she was just standing there. Husband took a month to get her back solid on a cow because she had been spurred and whipped so much for whinnying they had just about ruined her. After that, they started hauling her and she won a bunch of NCHA money.
I just have never seen a horse that did not gain a LOT from tying them out until they are completely accepted it.