Can I ask a perhaps daft question? How does a breeder select for 'good' traits? Is it a question of only breeding from dogs with the desired temperament/intelligence etc? What happens to the dogs who don't have these qualities? Presumably they aren't 'culled', or am I being naive? How can a breeder tell what an adult dog will be like when they are puppies? Do they hold back animals with undesirable traits, or sell them on? And if they do, how do they know that someone else won't breed from them anyway?
I'm not a breeder, I only have only ever had rescue dogs and collies at that but I do lurk on dog forums so I'll have a go at answering this.
For working dogs, in this case labs, the dogs will be assessed at a very young age for their working ability, their stamina, their readiness to learn and ability to use their mouths softly and be calm when it's required amongst other things. For show-type pups they must have no obvious problems that make them unsuitable for showing, and then they are assessed for 'type' and show potential. The young dogs who don't make the cut, but are temperamentally sound, will be sold as pet pups. Nothing wrong with that, they're well-bred and their parents should be healthy if they have proven working ability. Good breeders will have performed all the recommended health tests on the breeding dogs and have done their best to find the best mate for their dog, not just a sire because it's local, convenient or cheap.
If a dog has a really undesirable trait that will restrict it's life some breeders will put it down as soon as it's obvious. Others will sell or give away the pup at a reduced price if they find the right home. There is very sensibly, a condition that the pup must be neutered at maturity. Good breeders will take responsibility for the pups they produce for the rest of the the dog's life and should always take it back, what it's age.
Reputable breeders will register their pups with the Kennel Club as pedigrees, but they have an option to place a restriction on the registering of their progeny. This is an attempt to stop pet-owners from breeding their dogs. It doesn't always work as obviously they can't stop the dog being bred from, but it does cut down the profits of any pet-owner who can't sell registered dogs.