We should make the distinction about 'breeders' (and by this I have also meant reputable breeders who breed responsibly) as opposed to puppy farmers. Can we express it like that to avoid confusion.
Baskingseals -I see where you are coming from. You love your dog and want to have a continuation of that line. Lots of people have dogs who are parents and offspring. (One of my neighbours has a father and son pair of JRT although the father is such a bad tempered little bastard I can't imagine why they bred it.)
I don't see any problem with your contemplating breeding your dog within certain restraints (once) - you live in a rural area, and dogs are worked. Breeding between dogs who are well known to the respective owners and each other, where owners know of health and temperaments, is fairly responsible, for a one off event. I cannot know for certain but I imagine dogs bred in these circumstances are not in the same category of puppy farmed dogs. So I don't see an issue with this. You are not strangers to each other. But you'd have to have responsible ways of selling the pups. I would consider buying a dog bred like this. After all, the dogs have been selected on the basis of their work ability, or temperament, or health/hardiness. Many reputable breeders (by this I mean producing Kennel club standard show lines) breed for appearance or to retain a certain KC desired characteristic, and this is how a lot of deformities have come in. So this hobbyist breeding, done responsibly, could be OK.
Even dogs from reputable licensed breeders can turn out bad. There are no guarantees. Some dogs are genetically predisposed to certain characteristics, like Rage Syndrome in red cockers, or cavalier KC spaniels having heart murmurs or their brains growing too large for their skulls. I could go on.
Even before this dreadful incident, I had decided on never getting a rescue dog. Too much risk. Dogs who have been fucked up by someone else. I am not experienced enough to rectify that.
So we come back to there being too many dogs in rescues to ever stand a reasonable prospect of being responsibly rehomed. For their own protection, to prevent months and maybe years of languishing in kennels getting stressed out, then being rehomed badly by a rescue organisation, however reputable -aren't these dogs better off being destroyed after 7 days? Or maybe a month. Because there are no shortage of them.
Then, bring back licences. Make them expensive. There can be exemptions for elderly. I don't know how you'd means test it because it's not fair that poorer people can't have dogs and I don't want to discriminate against them. People like the homeless have dogs for self-protection, for example.
People out with a dog who can't produce a licence upon request -dog immediately confiscated and temporary stay in kennels, then destroyed. Painful at first but wouldn't this encourage more responsible dog ownership?