Maybe a complete ban would be a step too far, but honestly, with 10s of thousands of dogs in rescue centres, should people not really try their hardest to rehome one if they really want a dog? All breeds, ages, temperaments - all looking for a home and yet there are hundreds of back door breeders and puppy farms making thousands of pounds from inhumanly breeding fashionable dogs that quite often have health problems.
Some people are either too ignorant or stupid to do their research before buying a puppy. Maybe some people just want to bury their head in the sand because puppies are so cute right? They are also extremely hard work and will quite often find themselves in a rescue centre because someone didn't appreciate how much time they needed, or how much vet bills cost, or it snarled at their toddler so must be aggressive and has to be put to sleep.
Rescue centres are absolutely over run, while dogs are being held In horrible conditions and aggressively bred time and time again - and while people seem to be happy paying up to £1000 or more per puppy there will always be those going to exploit it.
Of course it's not just the dogs I mentioned above, any breed of dog worth a bob will be exploited.
If you really want a dog, do some research on different rescues and what they have to offer. Explore a breed or dare I say mongrel that you may have previously dismissed.
Having a dog in your life is one of the best things ever - but not at the detriment to other dogs so that humans can make some serious money.