It's not just a breeder problem, hell i've had some cracking dogs from both breeders of pedigree and breeders of mongrels (i love my pedigrees but i love my mutts as much so always have a mix).
The problem is the minority of bad breeders i.e puppy farms etc coupled with the muppets who buy a dog, go down the pub see their mates dog and see pound signs flashing

"lets breed our dogs call em a fancy name and flock em for £100's" they dont bother with health tests, temperament or anything else. Its just a way of making a quick buck!
It's too easy to get a dog these days and then worry about the consequences later, when the dog has behavioural problems through lack of basic training These people wont invest time and effort training it, they just send it to the rescue or take it for a drive and dump it.
Another example is the dog gets out and gets caught because "we couldnt afford to get it neutered"
"oh well let it have a litter we'll get rid of the pups somehow."
If you cant afford to get your dog chipped, vaccinated and neutered dont get the dog in the first place simple.
My idea re: licensing would hopefully get these idiots out of the system because its too much bother to invest in it. (i know it wouldnt work anyway as i said, but it is a nice thought).