Guard dog, I didn't create the standards for a breed. Every purebred was a mixed breed. After the mixture of breeds they determined that a certain traits were acceptable to call it a separate breed. If has the be able to reproduce the same traits consistently in or to gain acceptance as a breed. This is why designer breeds like the golden doodle is not recognized as a breed in any large registry. No one has been able to consistently produce litter after litter with consistent traits. Some look more like Goldens and other look more like poodles. I imagine that one day they will gain acceptance. But that will take a lot of work and science to figure out what percentage of each it will take to produce the same look in every dog in the litter. They will have to determine size, color, tail, etc.
Once this is established you don't continue to add breeds. You use dogs from the foundation stock and litters produced by the stock and their litters as long as the litters are from this point one breed.
Adding dogs from outside the breed is not reproducing the same breed. If you are going to do that you don't need to use a breed registry. You just have a dog.
With all respects this is complete nonsense.
Lets take your hypothesis even further and say after the Doodle has been accepted and is breeding true to type, they discover its a shrinking gene pool which it will be the minute they close the register. So the dog like many breeds today finds itself in a genetic bottle neck, after popular sire syndrome kicks in, thats breeding to top winning sires winning in the show ring. They become rife with emerging genetic diseases. They find the genes for some diseases and introduce genetic testing to help breeders but genetic bottle necks are such that there will be countless other problems involving possibly numerous genes in combination which can't be tested for or isolated. Fear mongering and a lack of understanding of science means they keep on at it pretending its diet causing the problems, other breeders, puppy mills, pet owners. Right.
Unfortunately they just keep on line-breeding and find there are no more dogs to outcross to anymore. Some of the diseases are so prevalent they can't even breed to avoid them anymore. They become diseased fait accompli. One particular gene is fatal but now all the dogs have it........Doberman. Right. They can't avoid it. Like the black colour of the breed, it's there to stay.
So an educated breeder decides to introducing to the gene pool either a labrador or a poodle or an F1 cross between the two to save the breed from extinction. This miraculously works in this hypothesis (given the genetics of both the showing pedigree labradors and the poodle its unlikely). This has always been an option, introducing another type but suddenly according to you somehow that has tainted the existing breed pool, making it no longer a pure Doodle??? Even though DNA tells us its the same breed.
Welcome to the lunacy of purists destroying pedigree dogs.