Interesting, I know what you mean, though, apparently all cockatiels as pets are all bred in captivity, none of them are exported from the wild i.e. Australia.
Cockatiels as Pets:
Small, intelligent, and easy to care for, Cockatiels have graced the homes of bird lovers for many years. Their engaging personalities and high trainability have put them near the top of the list of the most popular pet bird species.
When cared for properly, Cockatiels can be affectionate and fascinating pets. They are a wonderful species for inexperienced bird owners because of their natural friendly dispositions and curious playfulness.
Cockatiels are members of the parrot family, and have the ability to mimic. While it is possible for Cockatiels to learn a few words, most prefer to whistle or sound out noises that they hear in their environment, such as ringing telephones or doorbells. Sometimes their imitations can be quite convincing!
Temperament:
Mosy handfed Cockatiels have a very sweet, even temperament, and will exhibit a rather curious and inquisitive nature. They can bond closely with their owners and can be extremely affectionate. Cockatiels are quite intelligent and very social, and enjoy interacting with their human "flock". When properly stimulated, they are relatively easy to care for and make wonderful companions.
Like all parrots, they relish the times they get to spend with their owners -- they are very social and must be interacted with to remain tame. They should be handled, talked to, and played with every day to ensure their health and happiness.
We have two dwarf rabbits that are in their double decker hutch most of the day, except for evenings, and at weekends, when they go in their 'run'. And 'farmed' tropical fish (my charge)... that you might expect to prefer the amazon, yet do pretty well in our freshwater tank...
