It's not a class thing, it's a lack of understanding thing.
You don't need to buy a puppy - there are puppies in rescue.
Knowing a puppies 'parents' doesn't mean jack shit when it comes to training/suitability/temperament/disease.
Plenty of Rescues will rehome dogs to families with children, including babies. People just don't look hard enough.
There are plenty of pedigrees/pure bred dogs in Rescue, not just Mutts.
There are plenty of 'designer' dogs in Rescue, including all the ridiculous 'poo' crosses.
There is nothing wrong with having a mutt, pedigree or pure bred doesn't = better (and in lots of cases actually means a whole lot worse)
For most families a puppy isnt the best idea - house training a dog is hard, house training a dog with little kids squealing and shrieking about it is a bloody nightmare. Same goes with training.
Paying £600 for a Labrador doesn't make it a better dog than a £170 Labrador from a Rescue.
Every dog bred for profit sentences another dog in Rescue to death.