This assumes all mutations are negative. We have actually used intentional inbreeding to create hardier versions of various plants and we have also used it to create specialized breeds of dogs for better and worse.
The funny thing is, you need about 4 generations of incest with one common partner before shit starts to go really bad. ( Think cousins marrying, child is impregnated by father, child's child is impregnated by father or impregnates original grandmother. )
In a breed who you love society, short of being groomed for incest by your parents, this sort of repeated folding into generation 1 wouldn't happen. I mean, unless you're the British or Iranian Royal family.
Their kids will be fine.
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