My FIL had a parrot, awful bird. It would bite people and other pets, a real terror. Also demanded attention, if you ignored it you risked getting bit, if you paid attention it bit anyway. And they seem to live forever, he had it for over 20 years, when he died we had a real hard time finding someone to take it.
On the other hand I know people who have had ravens and magpies as pets and really liked them. As you say they could fly in and out of the house. Had a cousin who raised a duck from hatching, the duck imprinted on her and followed her everywhere.
Closest I have come was a pigeon, when we were kids my brother rescued it newly hatched from a cat. Nursed it back to health and when it got big enough released it. That pigeon nested on our house for years afterwards.