Many animals (including birds, dogs, horses) like the sanctuary and comfort of a cage and choose to use them, but obviously it shouldn't be used like a prison.
How did you arrive at the conclusion that birds like cages?
Even prisoners walk back into their cells. Comfort doesn’t erase confinement. A bird’s world is the open sky—so an open door doesn’t make a cage any less of one.
I would agree with that in most cases. They treat them like their personal house, unless the owner decides to reinforce their use as a form of punishment. Not really any different than building a dog house for a dog.