I'm not talking about selecting or isolating specific genes, or for specific diseases, as the genetic makeup of healthy animals isn't as simple as Mendel's wrinkly peas, but we should be able to select and favour generally healthy animals, that have a better immune response to a whole host of disease challenges.
Going back to our sheep, there is quite a strong showing contingent breeding for things such as markings or wool colour and neglecting more important traits. A lot of these issues mean we end up with cracking looking sheep, that work as a sheep because they can be supported with footbathing, trimming, extra feeding etc, but get them into our flock and they flake without all the added support that's been masking problems that have been bred into the flock, under the radar. And it only takes a foot problem to make them more susceptible to all the other disease challenges that might otherwise have been dealt with in a naturally healthy animal. Breeding from these animals is carrying the gene combinations forward & slowing overall progress.
What I'm perhaps not explaining very well is that the cost of screening stock is expensive so you don't want to be wasting it on animals that you should otherwise have culled out of the herd due to more obvious general health issues. I don't see a lot of evidence of this in Dexters generally - I've seen a fair few animals advertised over the years that are being sold as breeding stock that just don't 'look' healthy, even if there's nothing specifically up with them at the time.