For their own safety. I accidentially left the cage door open and when I came back my poor periquito, agapornis was on the floor and he was starving because he couldn't get to his comida o water :( I just like to keep them in a big cage so they have a lot of room to strech their wings.
If the bird is a pet, then yes, please keep the bird in the cage most of the time - not just a little bitty cage, but a nice big one.
However, if the bird is one that is not generally kept as a pet - ie a wild bird, I think it would be best to be left in the wild - unless tu have a rescue for hurt birds. Then of course till the bird is healed keep it caged.