Shelters perform cookie-cutter behavior testing that is designed to uncover fear biters and garden variety aggression. They frequently miss the mark on phobias, certain types of problem shyness, house-breaking issues, destructive chewing and dominance problems. Not to mention failing to pick up on hearing and vision problems which can both lead to behavior problems.
I'm in and out of shelters all the time and I have a lot of respect for the workers and volunteers but they are often understaffed and under-trained and turn over is HIGH. Many shelters don't have the time or staff to work with a dog long enough to uncover these problems. If the dog looks okay, acts friendly with staff, has normal interactions with other dogs and is mostly quiet, this is often enough along with a brief temperament test.
Two weeks later the problems start to emerge. Adoption is great - 3 of my Shelties came out of rescue, 2 of them by way of shelters that shunted them on to kill list. It's just not the best option for everyone.
And training issues never happen with puppies? Good grief... as a rescuer yourself, you should be the last to set back the efforts of rescuers by overstating that some of them need trained. ALL PUPPIES NEED TRAINED, so telling people they'd be better off with some pedigreed pup ignores the fact that any new dog owner needs to be prepared to train the dog they select, and stick with it for a long time, not expect them to be Lassie out of the box.
Again..the reason those dogs have issues is because they were neglected.
Breeders IMO add to the shelter problem you are talking about by bringing dogs into this world and selling them to anyone with cash.
I doubt most breeders screen their buyers.
A lot of these animals wind up neglected and living in shelters.