Rosielou: Thank you, your response is rewarding. The post above is a fundamental comment on a concept in the science of genetics. It is not specifically addressed to the issue of udder attachment. But this subject and your questions can be addressed in fundamental genetic terms. I would not want you to think "bad genetics" are thrown around. If they are in the genomes of mating animals, there are precise processes controlling where they end up. First, in the process of forming the sex cells (egg and sperm), then which the egg in an animals ovary is going through maturation and ruptures forth from the ovary on a 20 day cycle in a cow. Then there is the "luck of the draw" of which of the millions of sperm cells that get to penetrate the egg cell wall to begin the formation of the zygote.
Udder attachment, shape, size, color, texture, etc. is dictated by the genetic material in each cell. As each cell divides during the embryonic development, the DNA is telling the cell how to build proteins, fats, carbohydrates, etc. My son is working on his PhD on nothing but how proteins are built to demonstrate how complex this can be (gives the ole man a chance to brag, too).
It would not be possible w/o doing genetic mapping of the individual to know how long an undesirable gene will stay in the genome of a cow. But when you say gene pool, you are talking about the entire pool of genes in a population. That population could be the cows in your herd, the cows in your county, or all the cows on the planet. The concept of a breeding program is still the same as Mendel used 200 years ago. You cross breed, identify phenotypes that are undesirable, and try to eliminate them. At the same time, you look for the phenotypes that you want and favor them. There would always be a potential of the undesirable gene being cloaked in the genome by desirable traits.
I see misinformation on this board about genetics. But that happens even among geneticists. Breeding is not a pure science. It is not being conducted in a laboratory with fruit flies where all the genomes are mapped. Nevertheless, there are fundamental concepts of genetics that if a breeder does not have a working knowledge of, he/she could be making mistakes.
Let me say again to protect myself, these are genetic concepts that apply to all animals. You can apply it to udder attachment. But as a disclaimer, I am not a student of udder morphology, physiology, or anatomy. In particular, none of us posting have seen the condition that is the subject of the original post.
PS. Gregor Mendel, was not the father of breeding. He was the first one to use terms related to where the inherited traits were originating. It is general knowledge that selective Breeding is as old as animal husbandry. I noticed in reading the post that I could have been more clear on that!