Gonna be looooong....
I think it's a complicated issue and there several questions to consider.
Firstly, will the puppies find homes? In the UK each year, about 150,000 dogs go through rescue (I've taken the 2019 estimate and rounded it up quite a bit). Pre-lockdown, there were about 9 million dogs in the UK. If we assume that only that group of people will be in the market for another dog, and that dogs live on average 12 years, that means there will be homes for about 750k puppies and adult dogs each year. Even if EVERY dog in rescue is found a new home, there is still space for a minimum of 600k puppies.
Secondly, where do we want puppies to come from?
Puppy farms? Obvious no: the puppies don't get adequate socialisation, the conditions are often squalid, it's a terrible life for bitches being bred back-to-back and so on.
People who show or work their dogs? Maybe... But the show ring often isn't as focussed on temperament as it should be (though some show breeders obviously are), and a lot of homes are just not suitable for a lot of working line dogs. The show ring also tends towards unhealthy degrees of exaggeration, and high levels of inbreeding with a consequent loss of genetic diversity. Do we want to carry on down that road? I don't, personally.
People who breed small-scale for the pet market? Who own four or five bitches, and have three litters off each, so end up producing a litter or two a year (because one bitch at least will have aged out, and one will be too young). Possibly: they will be experienced and they will understand about the risk and the health tests and so on.
Pets? Someone who hip-scores the bitch, and makes sure that the stud is free of the known recessive genetic nasties in the breed, and has someone to turn to for advice? I really don't see why not: I've known several people breed in pretty much this set-up. They were careful about where the puppies went (and in one case, took a dog back). I'd rather take a puppy from that sort of background than from someone who had six bitches and who was bordering on puppy-farm territory, or a show breeder who ticked all sorts of boxes but whose dogs had terrible temperaments.
Pets? Someone who sticks two dogs together with $ signs in their eyes - well, obviously, no.
And of course, there are shades of grey between all those categories: someone I used to know bred cross-bred terriers with no health checks, a litter every few years. They were robust little dogs, who went to local homes, and at least one was taken back by that breeder (owner illness). The breeder didn't do it for the money: she always kept a puppy, and didn't charge a lot for the ones she sold.
What I would like to see is some sort of system where if you wanted to breed your bitch, you could pay a fee, do a course and pass a basic exam (when to phone the vet, the importance of early socialisation, etc), have a basic inspection (clean, secure, proper whelping box etc), provide any necessary health test certificates, and get some sort of certification that you could put on your advert so potential buyers would know they were going to a legit person for their puppy.