Yes, there should be strict requirements for being allowed to keep a parrot, the same for other large birds. People must use care to feed the birds, and maintain clean bird cages. It isn't easy, so a firm commitment is required of caregivers. Birds such as parrots are a joy to have around because parrots are intelligent animals, and some of them speak! Potential caregivers should be given a questionnaire at the adoption site, and be required to pay a fee. In these ways, agencies can be assured that the caregivers are serious, and that the birds will be well taken care of. If birds are abandoned, especially if they are in good health, they should be rescued by an animal shelter, with a chance to find good forever homes.
Once the parrot is home, the new owner learns about the mess, the noise, and the attention required. They don't understand bird behavior and socialization, why a bird will bite or scream, or its need for companionship (a flock). They are also often unprepared for the costs: feeding, toys, perches and veterinarian care. They are surprised that a parrot which should be easier to own - as it is kept in a cage - can be so demanding and that if it is let out, that it can be destructive.
Those that wish to buy exotic animals, like parrots, should be vetted carefully before being allowed to purchase these pets. Exotic pets require expertise, greater responsibility and more money than owning traditional pets. Therefore, before someone can purchase a bird like a parrot, one must ensue that he meets these requirements. There have been examples of people buying snakes and then releasing them in the wild after no longer wanting to care for them. This has upset the ecosystem in places like the Florida Everglades. In short, there needs to be a stricter vetting process for people that want to buy exotic pets.
People seem to love buying exotic animals, from tigers to alligators to parrots. But once the novelty wears off, all too often these pets get left behind. Alligators are flushed into sewers and tigers are sent to zoos. And parrots are returned to a wild that they didn't come from. I think that people should undergo a rigorous screening process before they decide to keep exotic pets. This will curb the buying of exotic animals and help restore our ecosystems to normalcy.