In my opinion there is no such thing as "humane" euthanasia, that is just a way of tricking yourself into thinking it's not really murder, because you believe they "didn't suffer", in the end it's still ending a life.
I understand what you mean about rehoming for the love of the animal, my mum breeds pure bred bullmastiffs and bulldogs, sells them desexed microchipped, all the four miles as you might put it. However there are some we keep, in order to show, socialise, teach others about the breed and occasionally breed themselves. However it gets to the point of too many dogs to effectivly socialise with and treat with TLC we desex and rehome them to a good home. We rehome them because we can no longer give them the tender tlc they deserve and because there are literarily hundreds of people out there hankering for a pure bred, and out of those hundreds, there are a select few who truly deserve one, people who can give the dog one-on-one attention, and pure love for preferably the rest of the dog's life.
However breeding an animal souly for the purpose of racing, regardless of what their life might be like at home, I cannot in any form understand or agree with. That's exploitation at it's worst, and disallowing the animal to carry out their true natural behaviours and the ability to socialise with other animals and people, something all animals, ESPECIALLY dogs need psychologically.
p.s, this is in no way an attack at anyone, just my opinion.