No one horse is crucial to the bloodline. There are LOTS of good studs. So far, they've deemed the purity of the natural breeding process more valuable than the ability to store and use the semen from a particular horse in perpetuity, even after death. If we all had an eternal supply of Secretariat semen, who would choose other lesser semen? What would happen to the gene pool then?
I would assume if the breeders know what they are doing, the offspring of the Secretariat semen should be improved versions of "Dad" and so thereby surpass the Secretariat semen. I suspect they want to allow nature to play it's normal role in the creation of the superhorse.
It would be almost like Dr. Frankestein otherwise. So, I am satisfied that this rule does make some sense.
AI is allowed in Labrador Retrievers, and that removes the practical limit on the number of bitches a dog can breed in a given year. When a dog wins, say, the AFC/NFC or the Grand, EVERYbody wants him in their breeding program. You wind up breeding animals with this dog all over the pedigree in multiple lines. In redneck terms, "His family tree don't fork."
Five years later, the problems crop up, and then everybody is worried . . . I have seen ads in Hunting Retriever News with the bullet point "No [famous dog's name here] in pedigree."
Allowing live cover only keeps a Triple Crown winner from being in EVERY pedigree and doubled and tripled up. And then of course there are the fraud issues and the risk of perpetuating a line that can't breed naturally.