Who ever heard of a bird-owner who kept it exclusively in a cage. Parrots are very affectionate.
True. But, only if they've been properly socialized. Dogs and cats can act just as wild if they don't have regular, loving human contact.
Parrots are also noisy, messy, bite and are unpredictable. When they reach sexual maturity, they often become very territorial over their nest and their mates. This is why some parrots, like certain breeds of cockatoos and african greys are known to be one-person birds. They pick one human as it's mate and defend it's territory against intrusion by man and beast alike.
Unfortunately, more people than you think keep their birds in a cage and never let them out. This is especially true after the bird reaches sexual maturity and begins acting like nature intended.
Since they're birds, we can't tone down their sexual behavior through spaying and neutering because their avian anatomy doesn't lend itself to these procedures. So, the only thing we humans can do is to either learn to live with them through the breeding season or give them up. There is no middle ground.