The fact of the matter is, the first time a horse is lassoed, it usually does fight the pressure pretty violently before it figures it out. Everything you see in the movies or at rodeos is horses that have been lassoed previously, and have learned to stop fighting and give to pressure as soon as they hit the end of the rope. The smart ones learn to stop when they feel the rope.
Many years ago, I had to have someone rope a weanling gone feral for me that we.could.not.catch after weeks of patient luring with food and treats. It was either that or start to withhold water, I thought the rope was the way to go.
THAT was an eye opening experience. The handler was tactful, patient, fit, strong AND very concerned with not hurting the weanling. He ran circles in the paddock after he got a rope on to avoid having him hit the end of the rope hard and hurt himself, then gradually reeled him in as he wore down. Even with all that, he had to be choked down in order for us to get a halter on him, after which we loosened the lasso, got him up, and led him to a stall.
Lassoing is only a gentle tool when the horse has learned to give to pressure and/or is used to being roped.
I don’t have a problem with the Brannaman photo. I would question the real world horse experience of someone looking at that photo and thinking it’s abusive.