A registry that offers no shows or performance events does not allow breeders to test their dogs as suitable breed representatives. In addition, anyone who buys a dog as a family pet want to ensure that the dog is healthy. Responsible breeders will ensure this by doing the proper genetic testing to ensure that the parents of their puppies are healthy. Less reputable breeders are unlikely to know that such tests exist, let alone do them. It is true that purebred dogs are subject to genetic maladies.
Different breeds have higher incidences of particular defects.
Responsible breeders are aware of what those defects are and will perform the appropriate tests to ensure that their breeding stock is free of defects. Pedigree analysis is a very important part of this screening. Responsible breeders can examine pedigrees to determine what defects may exist in a particular line so they can test for them and breed away from them. In contrast, dogs from an open registry may have a totally untraceable background. Even if they look healthy, their parents may have been riddled with disease.