In my mind, breeding a pet store betta would be a lot like breeding a dog from the pound. It might be a lovely looking dog, with a great temperament, and perfect health... but you do not know its lineage. Maybe its father was a top fighting pit and the pups will be dog agressive. Maybe its mother was a lab with hip dysplasia. Maybe its grandfather had Von Willebrand's disease. In short, mixed bettas are just as unpredictable as mixed dogs; you will never know what you will get from breeding, and thus, breeding would be irresponsible.
Most better breeders are part of the IBC for a reason; they believe in breeding only to improve the species. It is much like most professional AKC dog breeders would only breed to improve the breed. In short, breeders should want the most healthy, consistent, long lived stock, not just the most beautiful. While an LFS betta might be gorgeous - I have a PERFECT VT with gorgeous textbook finnage and colors - you have no idea what its lineage is, and so you can not even come close to guarenteeing healthy offspring.
The other paralell we see between betta breeding and dog breeding is the issue of overpopulation. How many millions of bettas are just rotting away on pet store shelves, because they didn't stand out enough to get grabbed up into the nearest vase or plastic cup? Bettas are probably the most universally neglected and abused pet fish out there right now, and to make it worse, there are tons of them. The type of people who would be willing to buy the offspring of a petstore betta are probably not the type of people who would give them the best homes, or use them to better the species.
In short, while I am sure your betta is absolutely lovely, it simply wouldn't be fair to its offspring to breed him/her. I like your idea of getting fish from good breeders if you choose to breed, instead. Just make sure whoever you buy from is reputable, well established, and preferably part of the IBC.