If getting a dog from a breeder is the luck of the draw, then there's something wrong with your breeder!
I've gotten dogs and cats from both breeders and rescue; right now any dog I get would come from a breeder.
Where I do think a breeder isn't magic is in the end behavior of the dog. But that's not because breeders can't predict temperament or personality--we actually can, to a great extent--it's because behavior depends on YOU. How you react to a puppy's normal actions, how you train, how you socialize, and so on can turn a sound, healthy puppy into a monster or a timid, retiring puppy into a fabulous, confident pet.
But any good breeder should be able to hand you a puppy and genuinely predict how it is going to look, what health problems or strengths it is likely to have, what food it should eat for maximum health, and so on.
And, of course, what you are really buying from a breeder is the next ten or fifteen years of that breeder's life. You're paying to be able to rely on that person to answer the phone at 3 am if your dog has a health crisis, to always be available to give reliable advice on anything from training to food to care to major veterinary decisions, and also to have a permanent, caring, good place for that dog should anything ever happen to you, to him, or to your life that means you can't keep him. A lot of posts we see here are about giving up dogs, or considering giving up dogs, or finding a new home for a dog. It's awfully nice to have somebody waiting in the wings, ready to take your dog if anything happens.
It's also true that responsible breeders don't contribute to overpopulation. We actually produce only a small fraction of the purebred dogs in the US, and no good breeder will ever let a dog or a puppy of that dog end up in a rescue or shelter. I have an extremely strict policy of never allowing any dog of mine to be bred without my permission (I retain rights that would prevent you from ever registering any puppy with AKC, and my contract states that you owe me a thousand dollars for each puppy that you produce without asking me first), and my contract is neither extreme nor unusual--it's what we all do.
When a family has young children and is considering a difficult breed, either one with major health issues or one with prey drive issues or aggression issues anywhere in the breed's makeup, I strongly recommend going to a responsible breeder over rescue (breed-specific rescue is fine).
And thanks, MamaAllNatural