One of the primary arguments advanced in favor of keeping parrots as captive pets - which so often ends in years of bitter suffering for the parrots - is that captive breeding maintains a genetic reservoir in case the bird becomes extinct in the wild. Leaving aside the fact that some parrots are endangered solely because of the "pet" trade, the argument is only valid as far as it applies to ethical breeding: selection of proper stock, not propagating birds with genetic weaknesses, proper training so babies don't die if they must be hand fed, proper medical care and pleasant living conditions for the birds.
Do I care if you mix a poodle and a collie? Not at all. In the first place, they aren't separate species, just cosmetic variants of a single one. Domestic dogs aren't going extinct in the wild because they don't exist in the wild. But if you breed a poodle and a wolf i begin to feel uneasy. If it's an interesting mix it will happen again, and the chances are some poodle lover will wind up with adult woodle that he can't manage, and it gets put on a chain in a backyard, or sold to a "good home" that is really a dog fighting ring. If there is a move to reestablish breeding wolves into a prior range in the wild where they are now extinct, these hybrids could be a source of gene pollution.
With parrots, the ONLY advantage of a hybrid is human pleasure - to satisfy curiosity, to possess something unique as a source of pride, or for the pleasure of looking at them. Are any of these intrinsically wrong? Let's not say wrong or right....but the human tendency to chase after novelty, pride and pleasure does not always work out well. We must have he newest shiny thing, and when it becomes worn as all things do it goes in the trash. Which often means polluting the land, the ocean, or poisoning the people who recycle the valuable parts. Plus it takes fuel to extract the raw materials and to make the thing in the first place, hence Dakota Access Pioeline, oil sand devastation in Canada, drilling in the arctic refuge, you get the picture. Indulging our desire for pleasure does not usually benefit the earth. Or us either. Who becomes more patient, more loving, more compassionate from getting a new iPhone every six months? How does it help us become more mindful, more aware? Is it legal to chase after pleasure? Of course. Does it build character and wisdom? Maybe not so much.
Chasing pleasure is not the same as pursuing happiness, or as taking pleasure in life. I can enjoy a beautiful sunset, and get out of my chair to go to a better vantage point, and that doesn't hurt anybody much. If I drive to the top of the hill in the next county, that does cause a little more suffering - I need a car, and gas etc. and my actions in concert with a million other people doing the same thing has a real impact. If such a simple thing has complex repercussions...it's hard to keep thinking about it...no wonder we have so much TV/internet/booze/heroin/texting/etc to distract us.
So cross-breeding captive birds, yah, it has repercussions. Take African Grey parrots which are terribly endangered in their native habitats because of illegal trapping for the lucrative pet trade. Forget for now how many suffer and die in the wild, during capture, during transport, in being forced into unnatural environments with humans who don't know or don't care to treat them right. I'm not seeing any upside for an intelligent bird in this. Oh, but captive breeding to the rescue, it maintains the gene pool, keeps them from going extinct, no more horrific poaching and trafficking! Well, then maintain the gene pool...don't breed defective birds...don't sell them to unprepared or uneducated humans...keep a record of the lineage to prevent inbreeding. Which won't happen because it interferes with our right to make money on stupid birds, for crissake, I can't afford to do all that, I just got these two siblings and it's my right to breed them if I want to and if someone wants to buy them. Right? Who cares if I only got a CAG and a TAG, a gray bird is a gray bird. Right?
With an endangered species it becomes even more important to keep the captive gene pool as pure as possible. One hybrid of itself doesn't do any harm, other than reduce the size of the pool, but if it becomes popular and everybody starts to want one that's a problem. If it breeds back into the pure population it's a problem. Now you have introduced subtle and major genetic changes into the species which will be impossible to remove and make any future reintroduction of wild populations difficult.
Hence the arguments made against, hence the repeated asking "what's in it for the birds".