Re: boarding mares on site. Most KY farms house their stallions separate from their mares entirely, either a different section of the property or a different parcel of land with a different address. So mares are vanning back and forth to the stallion even if they are boarded “on site,” which is different than most other breeds. As others have said, everything is so centralized in KY it’s not a big deal. There are only about a billion places to board a mare within a short drive of all the major farms.
Outside of KY in other states, most farms are all on one plot of land- it’s less likely to have to van the mares to the shed just for breeding, it’s more a matter of pulling them out of the pasture and walking to the shed. With the exception of a few regional epicenters (Ocala, for example), the different breeding farms are separated by a lot of distance. So mares are more likely to be boarded at the farm with the stallion unless they happen to reside nearby.
Even with reproductive advances, 253 is a huge number to appreciate. I find it funny that anyone can dismiss it as merely improved technology. Most farms are not at that point. Then again, most farms don’t go to the shed 3+ times a day. I’ve been at Ashford when the line is around the block just because of the volume of mares their stallions cover.