This sounds completely backwards to me. It teaches the horse repeatedly that if it doesn't get away the first time to just pull harder and eventually it will work. This would be a way that a horse might actually hurt itself. Much safer to teach the horse the FIRST time that it can't get away.
This method came from an Australian horseman called Tom Roberts who spent his lifetime curing "problem horses", and this method worked very well for a number of horses that came to him with the "won't tie up" problem. I haven't explained the method as well as he has in his "Horse Control" series, and the thinking seems counterintuitive at first, but I think he "gets" how horses process, and I've had a lot of good experiences with his training tips for curly situations. I know several people who tried this method themselves and had it work for them. I guess it depends on why your horse won't stay tied.
The tyre idea came from Robbie Murray, who pioneered horse "gentling" rather than "breaking" methods in Australia in the 1970s. She doesn't seem to have had any rodeos as a result of using her tying method, but she doesn't do this stone cold either, she does it at a certain stage of her training process.
I'm not a fan of tying horses unbreakably. My horses tie fine as we speak by the way. I also have a mare who was difficult to tie for years - in her case because her first experience of halter handling (before I bought her) was someone tying her unbreakably to an unbreakable object as a yearling, and flapping at her with an oilskin until she was in a lather, to teach her, "When you're tied up you can't get away." Thankfully she didn't break her neck, but she was headshy around people she didn't trust for her whole life after that, and nervous about being tied. For her, tying her with more play in the lead than with the average horse made her happier after her early traumatic experience. I just wish she'd had her halter and tying training with a gentle method, because it would have saved a lot of hassle down the track.
However, if you truly have a horse who has learnt the cause-and-effect of tying up and is really deliberately breaking away, this is a different scenario to what went wrong for my mare. It's just that I think a lot of people assume that horses always
know what they are doing when they break backwards and are doing it deliberately to get free, when this is not always so - and when this is not so, then injury, drama and bad conditioning may result from force-tying a horse.
My father educates a lot of young horses and never force-ties them in their education - he also uses a gradual method, and has only had one horse in the 30-plus he has worked with who has truly tried it on in this department.
Anyway, just offering a different perspective!