Great list and discussion, to which I would just like to add a couple of things.
When it boils right down to it for me, as to what separates a reputable breeder vs. everyone else (whether mill, BYB, or registered breeder who passes on pedigree papers but "on paper" only) is responsibility; responsibility not only when it comes to the betterment of the breed and all that that means, but also responsibility when it comes to each and all of the pups and kitties ("charges") that they breed, I agree, and to which I'll add that the Club to which they belong is itself responsible, meaning: the Club itself has and/or is connected to a separate rescue "wing", an independent non-profit, being dedicated to finding and placing animal members of the particular breed for which it speaks, and educating the public when it comes to the good, the bad and everything in between as it pertains to that particular breed as well.
Such eductation would include (and always) the general need to spay/neuter and thus further hammering home the (contractual) need for same, and which responsible breeders and responsible buyers agree upon in their contract in first place (and actually follow through on same). In turn, coming full circle so as to provide a true network of support for all concerned, including: individual breeders themselves so as to have among other things assistance in the event one (or more) of their charges are returned for whatever reason by the owner(s) due to a change in circumstances such as illness or death of the owner, divorce or whatever the case during the life of the animal, as well as support in terms of ongoing education and so forth when it comes to training and other advice (including resources and referrals) as may be helpful to buyers and interested members of the public as well; this, so as to maybe actually help owners keep and enjoy the companionship of their pet for-life, instead of relinquishng same (where circumstances warrant, sometimes pets are far, far better off being relinquished and placed in a new home, if you catch my meaning, but hardly is this true in all cases, or at all).
As to getting a young pup or kitten spayed or neutered, this is controversial, and it is best the animal not be spayed/neutered when it is too young and still growing, arguably needing its hormones, etc. in tact for proper growth and development. Yes, shelters and some rescues insist upon early spay/neuter to "guarantee" that it's done, saying that the benefit (reducing pet over-population) outweights the risk (health and growth of the animal, etc.), but not something I personally support or believe in (unless and until there is conclusive evidence that early spay/neuter results in no harm, as in none, which simply is not yet the case, and why it's controversial). Rather, responsible breeders and rescues will (or should) insist upon a deposit, which varies but typically around $200, which is refunded to the buyer/adopter on proof by means of a vet certification of spay/neuter when the animal has come of age (around 6 months of age, give or take depending on the breed and its actual development needs), it also being a good idea for breeders/rescues to send out to the buyer/adopter "helpful reminders" and further follow-up on as well.
Finally, as to rescued animals, the vast majority of which have been relinquished (dumped) by no fault of their own, and are great pets. The chief reason why so many great adoptable pets wind up in rescue is because a buyer (some human) didn't bother to do any research on the breed in which they were interested prior to purchasing same, and the concept of picking up a phone and hiring a trainer or other such assistance is foreign to them and/or, and quite simply, didn't bother to spay/neuter! Luckily, there are reputable rescues (as well as reputable clubs connected with a rescue arm if you will, thus responsible breeders in turn), as well as responsible members of the public. Many people actually are quite happy to avoid the "crazy" puppy/kitten phase altogether, and also find rescue/adoption of a perfectly adoptable pet animal from a responsible shelter or rescue to be incredibly rewarding all-around as well (and please note: responsible shelters and rescues only place adoptable pets, and only then in deserving homes
Then, if everyone in the whole and entire chain was responsible, I will actually risk going out on a limb here to say we wouldn't have a pet over-population problem in turn, and in such a world pedigree papers would mean all that they should and then some. What a great world would that be, I agree, and a great list to help us all get there all-around as well!