We have a dog and a cat, both rescues. The cat was just a kitten, a little fuzzball found on the side of the road. No one claimed him and he ended up here.
The dog was a stray as well, not tiny but still a puppy. He too went unclaimed and ended up with us.
Neither one has had problems from past trauma that we have seen. Well, the cat can be a PIA at times, but that’s just being a cat.
All that said, you make a good point. I’ve also seen plenty of dogs which aren’t abused but which have been allowed to develop bad habits. Some of them would be very unpleasant to live with.
One of our best cats was a rescue, but their insistence on the hysterectomy at 5 months killed two of the 3 female kittens in her litter. It nearly killed her. That is way too early for such surgery. But she was eternally grateful we saved her sick little life, and at that time we let cats go outside. She was the killer hunter of any cat I have known. She could catch and kill anything.