We are not talking typical 'bad behaviours' for one. And two the sort of people who can handle extreme behaviour problems are very few and likely already have dogs (or don't want dogs with problems) And three, (and biggest IMO) In the year(s) it takes to maybe fix one dog hundreds (thousands?) die that could have been helped in that time. There comes a point when you need do save the most you can.
Let me tell you the story of Sammy...
Sammy was a young JRT who came into rescue. He had a conflicting story, he was supposed to be highly aggressive, and had bitten, but people who met him said he was sweet. Then he went to a foster home, where they said he was crazy. The person who transported him to me said he was adorable and sweet, he was fine with me on the way home. He was fine when he met hubby the first time.
Next morning he acted like he wanted to eat hubby. So we did TONES of work with him. He was fine with all women and kids just hated men. I had all food come from hubby. Sammy was fine as long as there was food. As soon as the food ran out he would freeze, and look up and thank doG I had him on leash!! He never got better.
To add to this he would shake, not the nervous dog shake, I have had a few JRTs come in that do that. This was like an excess of energy shake. He could do swimmers turns off walls at chest height. I could scale almost anything and what he couldn't scale he would attempt to chew through.
Then one day he decided he wanted to eat kids. NOTHING had changed. Bet my life sort of sure that nothing had happened. And when this dog hated things he lost his brain. He would foam and air bite and spin in his crate if he saw the object of his 'hate'. He would grab the bars and pull till his gums bled. He would fling himself at the door.. even after the person left he would continue for a while. It was scary.
So what would you do with such a dog? The rescue seriously though about seeing if they could adopt him out to a lesbian couple. But I said this dog is a high risk at getting loose, and unlike dogs with fear issues.. he would fixate on the first man or child he saw and attack. Even if someone wanted to take him he was too large a liability for the rescue to adopt out.
Taking him in to be PTS was heartbreaking. He was still happy with me....