I knew one family that ran dogs for coyotes (and coons, fox, etc) but they got out of it a few years back. Logistics and upkeep just got too complicated and expensive. It was also time-consuming in the extreme because once you cut them loose, you’re going to be hunting until the last dog is collected. Which could be 2 days later.
As far as breeds, they preferred thier own cross-breed. It reminded me of the way sled dog racing is now where the breeders are not hide-bound by purebred showdog thinking and they are looking at each dog for what it has and then when they want more speed, stamina, or drive, they breed up the two dogs that they think have that to see if they get more of it.
Grouse