The problem is that there are approximately 3-4 million dogs and puppies in shelters yearly. Of those dogs, 56.4% are euthanized.

Is that clear enough? It's a matter of ETHICS, not physical "rights and wrongs". Is it ethical to breed litters of mixed breed dogs for the sole purpose of "companionship" when there are literally 3-4 million of these type of dogs languishing in shelters every year? As much as you want to live in your fantasy world, not every one of your puppy buyers will be able to provide a stable home for life. It's the hard, cold truth. And I'd be glad to discuss this with you 5 years from now when your dog's puppies are no longer cute and fluffy and when their owners are going through life problems like marital and moving issues.

But since you don't seem concerned with the ethical implications, let me lay it out in a medical sense:
Are your and your friend's dog tested for every single possible congenital disease? PRA? Luxating patellas? Do either of your dogs have a genetic predisposition to epilepsy (this is, by the way, impossible to determine without a pedigree)? Do they have genetic predispositions to cancer (again, can't determine without a pedigree)?

What will you do when your dog's puppies suddenly develop these health problems? If you can deal with the guilt, go ahead - breed. Personally, I can't subject other dogs to die while I breed potentially unhealthy puppies.