From an Arab perspective:
When I first got interested in Arabs lots of breeders were inbreeding to *Raffles, the result of a father/daughter breeding (Skowronek PASB x Rifala, his pedigree was provided earlier in this discussion). When the Polish Arabian invasion came to this country the *Raffles linebred/inbred horses had problems that were greatly improved by out-crossing to the Polish Arab lines, just like the original very inbred/linebred Blunt Arabians were improved by outcrossing to Egyptian Arabs and how the heavily linebred Blunt/Egyptian Arabians were improved by outcrossing to the the Polish Arab Skowronek, *Raffles’ sire, at the Crabbet Park stud in England.
Eventually the only way to improve an inbred line is to out-cross.
I was in a VERY inbred/linebred Arabian breeding group, the pure Davenport-Hamadie group. I could find faults of the original imports in my horses over 70 years later, like *Abeyah"s long sloping pasterns (that can eventually break down even without heavy work), *Muson and *Hamrah’s underslung necks, *Reshan’s too short neck, etc., along with other faults. Don’t get me wrong, the Davenports can be wonderful horses, they just are not perfect and the line/inbreeding does not help their imperfections. This group has been heavily line/inbred since 1907 except for the accidental introduction of the Hamadie blood in the very earliest days of the Kellogg Ranch (two mares were misidentified, one pure Davenport, one a Davenport-Hamadie Arabian, the later ended up breeding on in the “pure” Davenport group as well as in the general Arabian population.)
The other Arabian population that has been heavily inbred–the Babson Arabians linebred to *Fadl bred to just 4 or 5 imported Egyptian Arabian mares. I think this group has been closed to outside blood since the 1930’s (?).
Before diving in to what is essentially in-breeding light I suggest that you study these groups to see the possible long term effects of this type of breeding.
For another breed, the pure Puerto Rican Paso Finos ALL go back to the stallion Caramelo on all the sire lines, which is a big reason why they got out-crossed with the Columbian Paso Finos up here in the USA, to get a better horse through hybrid vigor.
Inbreeding is like an original sin. REALLY tempting, but in the long run not a particularly great idea if you want sound horses that are usable for performance down through the generations. Believe me, eventually the faults of the horse that is being inbred to WILL come out in at least some of the horses in the future generations, and unless there is ruthless culling these faults will continue to reappear forever. The only reason the TB successfully survived its great inbreeding is that four different breeds of horses went into the original TB, which meant that the TB had a much wider gene base than the Arabian lines in Europe or the USA, or the Puerto Rican Paso Fino lines.