@Pickle and Tigerlily,
When I first started having birds, I lived in a small apartment in the Bronx. We had one bird at a time, each was in a cage.
My family and I moved to a larger apartment, and I got more birds, which we kept in cages. They were all trained in cages and allowed out. I remember that we clipped their wings until they were trained. In looking back, I'm not happy about that, but it made it possible to train them outside the cage without them flying away. I don't remember much more.
Side note: Our first parakeet, Billie, laid many eggs. They were unfertilized. We tried getting her a mate, but ti didn't work out.
Second side note: Year later, one night during dinner, Melvyn mounted Bambi. My mother had a fit. No more birds!
In both cases, we let nature take its course.