Expanding the gene pool reduces the odds of disorders caused by recessive genes (e.g. hemophilia). Beyond that it depends on the species. Domestic animals are more highly inbred than wild populations.
Humans have less genetic variability than most other large animals. We are literally more alike than we should be given the size of our population. The most common theory I've seen put forward for this was a genetic bottleneck. Around 70k years ago a sudden change in the climate reduced the human population to perhaps as few as 10,000 individuals.
Late Pleistocene human population bottlenecks, volcanic winter, and differentiation of modern humans
Or, Look up "Toba Super Volcano".