"Genetic mutations?" What, like all species on the planet? Of course they have genetic mutations (or adaptations) but that doesn't mean to say you can't improve the breed.
Don't mean starting all over again, but reintroducing some slightly more powerful, robust stock as most breed societies allow to improve the breed and correct its deficiencies. Which in the TB racehorse include breaking blood vessels at exertion and bleeding, breaking down, increasing lack of substance and shortening of race distance, plus inbreeding to the Northern Dancer and increasingly Storm Cat lines to produce fast maturing two year olds or even horses that mature quickly enough to be sold for millions at the sales as yearlings.
Unlikely to happen in this lifetime but in 100 years, I can't imagine the TB racehorse being in a good state as a breed and people then perhaps thinking about outcrossing.
By the way, the Secretariat male line is effectively is already lost. Wouldn't be commercial enough now to breed a horse with that amount of stamina.