There is a certain AFC/NFC/GRHRCH Labrador that is doubled and tripled up in so many pedigrees, that the ads in the UKC Hunting Retriever News now tout that he is NOT in the pedigree of the dogs offered for stud.
Of course, artificial insemination made it possible for this boy to breed way too many bitches -- far more than he could have covered naturally.
It's even true when AI is NOT allowed -- there is a Seal Point Siamese male that appears all over the pedigrees. I was at the Atlanta CFA All Breed show the year he bit right through a judge's hand (I was standing outside the ring waiting for the Blue Points to go up.) He had the most hideous temperament I have ever seen in a Siamese - and that's saying a lot, they are "tetchy" cats. But everybody bred to him because he was gorgeous and a Quadruple Grand.
When I purchased a young male kitten I took a look at his seven-generation pedigree, and noted with some unease that this cat appeared right at the back of the male line. I bought him anyway, because his mom was the most laid-back cat I had ever met (a mother cat who would let a total stranger pick up her kittens from the queening box, and smile at you while you did it . . . ) Amazingly, he turned out to be a mild grouch, just a mild grouch, but a little mean nonetheless. He's the only one of my cats who has ever bitten anybody (my husband and my son, and both of them had it coming . . . )
Oh, I know what you mean about siamese being tetchy! My aunt and uncle had one when I was growing up....scarey cat! ;)
ANyway, in goldens we've had a couple of very prominent sires. Nice dogs, with good stuff to contribute, but like all of us with some negatives (we all have some bad genes!). And, as you mention in your cat example, we see whatever those traits were all over the gene pool now. It's too bad with dogs. Imagine the effect if it's a human gene pool? (in fact, makes you wonder if some of the lethal genes in certain human populations might have come about in a similar way, a prolific ancestor who happened to carry that gene).
susie