I have two lovebirds that I rescued about 7-8 yrs ago. They are in a 2'X 2'X 3' cage and are never out. First, my cats would eat them in a heartbeat, and secondly, they are monsters. They can fly because they have done that at the vet's office but they don't seem to choose to 99% of the time. They climb with their beak like parrots do.
That's how I lost my parakeet. It was really a bad scene... I was in college with two roomates in a house. The bird was always loose in the living room, either on a plant or on/in his cage that hung from the ceiling.
We had a stray kitty we were feeding outside, and another friend backed over it, and broke the cat's leg. We took kitty to the vet, who put a cast on the leg, and we had to keep him inside. We'll the cat was gimpy, the bird was pretty astute, so for awhile it was OK.... but when the cat got better, it stopped working. Too many members of the food chain in the house. :~\