@EdwardTeach
This is a question that occurs to me whenever I see an MN thread about people paying thousands of pounds for a dog these days. When I was a kid almost all the dogs I knew were mongrels that could be adopted cheaply or for free from local farms or the like.
I think it's because people's attitudes have changed in recent years.
It's no longer acceptable to let your dog wander the streets or fields unattended, so the likelihood of a random mating occurring is much lower than it used to be.
It's also much more common to get your dogs' neutered and spayed at a younger age, especially bitches. Most people spay their bitches after the 1st or 2nd season to avoid the risk of illnesses like pyometra or mammary cancer.
The increase in dog walkers/doggy daycare probably also has something to do with it - many won't take entire males and bitches in season can't attend either, so it's more convenient to have your dogs "done".
But saying all that, mongrels still exist, but if you dare tell someone that their cockapoo/labradoodle/cavapoochon is a mongrel, they get all up in arms about it, even though the definition is "any animal resulting from the crossing of different breeds or types." So, any crossbreed, basically.
Nowadays mongrels are the new trend - they're just called designer dogs so they cost several thousand pounds instead. It's much, much cheaper to buy a labrador, a poodle or a shih-tzu than it is to buy any of the existing "crossbreed" mixes out there.