but hte dog "correcting his own mistake doesn't get a reward. Just avoids a correction. There are many different parts of dog traing +P (giving a reward) -P (withholding a reward) +N (giving a correction) and -R (withholding a correction) Balanced dog training uses a mixture of all 4, depending on the situation.
I can tell you several fields that don't use alpha theory - police dogs, search and rescue, detection dogs, service dogs of various sorts including guide dogs for the blind. All give corrections, sure. But none of them use alpha theory. All of these are fields where you want the dog to be right 100% of the time but you can't use corrections once training is over. Plus, with apprehension dogs in Police work, you need a dog that thinks he is 1000% king of the world, could take down King Kong if you asked him to, and will keep his grip despite being hit, kicked, stabbed, or even shot. So physical corrections to a dog like that are nothing. The biggest punishment for many of them is the training session ending before they get to take down the decoy. Or disappointment for their handler. Also, the dog must have 100% certainty what is expected of him from a given command, must obey immediately and the handler must have 100% certainty that that will happen. He must put his life in the dog's hands and trust. The dog must do the same - face down the threat with the knowledge of what is expected of him and knowing that the handler is his partner.
Part of the "alpha theory" problem is the belief that a dog does things out of a desire to be dominant. There are actually very few dominant dogs. There are, however, a lot of insecure dogs that will take advantage of a lack of leadership and throw their weight around because they don't see anyone else as being in charge. These dogs are easy to spot because they are always doing "dominant" things like trying to hump other dogs, trying to "stand over" other dogs, being pushy with their owners and others, etc etc A truly alpha dog doesn't do any of those things except as a last resort. 99% of "problems" are solved by a simple look and the other dog offers submissive behaviors.
As I said, what you are describing isn't alpha theory. It's balanced dog training. Alpha training is something entirely different. Alpha theory is a "hammer and nails" practice - when the only tool you have is a hammer, then everything looks like a nail. Meaning that alpha theory is based on the idea that your dog wants to be the boss and you must regularly put him in his place through the use of corrections. When that is all that is in your toolbox, every interaction with a dog is you vs the dog.