In response to the original question, there is a good argument to be made that carefully chosing parents within a breed may be able to do better at avoiding disease risk variants than random “oops” pups as in both cases natural selection has effectively been removed. But the important difference between purebreds and mixed breeds is lack of genetic diversity in most pure breeds.
Note that a large portion of genetic variants that may predispose a dog to disease are recessive: a dog can carry one copy of the variant and not be impacted – or at least not impacted nearly as much as a dog with two copies (one from mom, one from dad). The odds of a mixed breed dog having both parents be carriers of the *same* harmful variant and getting the harmful variant from each parent is exceedingly small. Within a breed, in contrast, there is much less genetic diversity, so if a potentially harmful variant exists, it exists in a lot of the dogs in that breed. So the odds of both parents each being a carier of such a variant is much higher.
Breed clubs can make good choices on which dogs should be used for further breed and which may not be suitable. But even under the best of circumstances, this leads to a diminishing gene pool, so eventually even if only the best possible pairings are being bred, there are simply so few possible pairings to chose from that “the best” may not be as good as we’d want it to be.