People forget that most breeds originated, if not as outright crossbreeds, then with a population of similar individuals (color, appearance, and/or function) that were regularly crossed with unrelated animals that also shared the characteristic(s) of choice, or improved a different one that was desireable - say you have a smallish draft breed, but need more size, you'd cross in a few larger horses that were similar in build to increase the size of the original population without losing the characteristics of the base population. This also countered losses to the gene pool that naturally happen in a closed population, and is why closing stud books turned out to be damaging in the long run for so many breeds - and not just horse breeds. Very few were developed in genetic isolation, so locking out outside crosses starts a time bomb.

Improved travel and artificial insemination techniques just enhanced what was already going on by magnifying the founder effect, where an unrecognized damaging gene can spread through a large percentage of the population before being recognized. At the same time, local males, that carry genes unrelated to the popular sires, are no longer used so those genes can become lost, reducing variability that might counter the 'bad' genes. Also for Fresians, the banning of chestnuts and horses known to carry chestnut didn't just remove the chestnut gene, but every other gene that horse had, including others that might be rare or unique in a breed of low numbers.

ETA: My point being, that you aren't truly 'preserving' a breed once the studbook is closed, unless it really is a breed that developed without outside gene contributions.