I think that the whole "Breeding mutts is automatically irresponsible" is a bit too much of a blanket statement for my taste. Where I'm from, breeding mutts with strong, functional, working traits is fairly common. So I shall look at this practically. Before you consider breeding, take a look at this:
-Are both parents health checked? I don't mean "has all their shots and looked over by the vet". I mean thoroughly screened for hereditary problems, like eye problems, luxating patella, hip dysplasia, etc. Keep in mind that each of these tests costs hundreds of dollars to complete.
-How are their temperaments? Are both parents steady, dependable and confidant? You don't want to breed dogs that have aggression issues, are very shy/nervous, excessively submissive, poor social skills, etc.
-What do the parents have to offer? Are they outstanding working dogs? Great at obedience? What titles have they earned? Or, if they're more of the "lap dog" type, do they have the great temperament and loveable personality desired?
-Can you take the mother for necessary health exams, X-rays, etc., during pregnancy? Can you afford an emergency C-section if necessary (usually $1,000 or more)? If problems come up, be prepared to hand-raise if necessary. Be aware that there are many complications that can occur. Breeding is dangerous for the mother as well as the puppies.
-Breeding puppies costs money, even for those who breed expensive show dogs. Expect to lose money in this venture, not make a profit. You must give the puppies regular check-ups and shots before they ever leave your care. And since your puppies will be mutts, you cannot charge anywhere near as much as purebreds (unless they have specialized working skills).
-Do you have time to teach these puppies? Learning begins long before they leave to new homes. Get them used to strangers, "normal" home noises (like the dishwasher or doorbell), how to handle grooming, and the beginning stages of crate training, leash training and housebreaking.
-From the tone of your posts, these puppies will basically all be going to relatives for companions only. Will you provide spay/neuter contracts? That would be the responsible thing. While these puppies may have guaranteed homes, that doesn't mean any of their puppies will.
-Are you willing to take responsibility for the dog for the duration of its life? That means you will take a puppy back for any reason, at any stage of its life. You brought the puppy into the world; you are responsible for making sure it has the best life possible.