And here we have the root of the problem. The person who took that puppy didn't want it any more, or didn't care enough about it to find it when it got out. There is no over supply of dogs - what there is an oversupply of is people who are not committed to keeping the dog, people who did not train the dog, people who did not carefully consider before they took the pup.
The problem begins with the breeder, whether cross bred, purebred, or designer mutt. If the breeder does not qualify the homes for the pups, and ensure that the home is the lifetime hnme and just sells to anyone, there will be dogs in the pound.
Bit off topic!!
All dogs deserve good homes. Anyone breeding them should be aware of that. They should not be bred unless that can be guaranteed. If unspeyed bitches become pregnant, and the owners do not think they can find all the pups homes, the bitch should be speyed early in the pregnancy.
Unfortunately, it doesn't happen.
It's all probably not about cross bred and purebred, it's about responsible breeding, no matter what it is, and responsible homing to well chosen lifetime homes.
If you can't do that, don't breed.
JMHO