Sucked back in...
I asked if you knew anything about genetics because you were writing as if you had no idea at all about heredity or inbreeding.
When I did the agricultural revolution at school we taught about animals being selected to be bred on the basis of their attributes - which implied that the second-rate animals (the low-yielding milk cows, the undersized plough horses) were not bred.
And again - and I am being polite here - your suggestions don't seem to reflect an understanding of genetics.
My solution would be to have a number of allowed breeds and that's it.
All dogs bought from registered breeders of the allowed type,
No cross bredds so no confusion on what sort of dog it is etc.
You've made it plain that you want only 'useful dogs' to be allowed, and it has been pointed out that, never mind the rights of people who enjoy owning pet dogs, there needs to be a population of pet and sport dogs to underpin the working dog population (to absorb the ones who aren't suited to work, to provide advances in training, to keep a wide gene pool, to preserve traits not currently wanted in the working population but which might one day be useful etc etc).
As for never allowing cross-breeding... if the world's various kennel clubs don't wake up to the dangers of shrinking gene pools, they are going to back a lot of breeds into a corner, which might please you as breeds would go extinct. If you constantly breed within a closed gene pool, deleterious alleles have a nasty habit of becoming more concentrated within the population. These are usually recessive
(because the dominant ones make the animal sick so are usually more obvious and can be bred away from) and by the time the realisation dawns that a new disease is popping up, a large proportion of the breed can already be carrying the problem allele. However, various KCs do seem to be waking up and there are various sanctioned outcross projects popping up around the world.