What you say matches my experience! It's really funny when you hear a bird "muttering" to itself, they almost seem human. Also when it gets excited and lets out a loud beep!
This one lives more like a dog or a cat. Flying around the apartment as he pleases. The only time he goes in his cage is when it’s safer for him (or us, parrots bite when displeased).
Funnily he gets very angry when his cage door is closed and he’s outside … even though he never goes in there. But he might … he does ask to be caged when it’s bed time. It’s quite endearing.
Does he try to run away if a window is open ? Or are they similar to outdoor pet cats?
So, yeah. I made sure there was generally something on the floor below them. But the sides of the doors would need to be cleaned fairly regularly. I had cockatiels, and you couldn't "potty train" them.
Birds also like to chew things sometimes, so you needed to keep a close eye on them or realize your damage deposit was going to take a hit later.
He does poop everywhere else though. Usually in a few common spots. Fortunately it doesn’t smell and we just wipe it with a paper towel.
Training him to poop in sinks had limited success. We aren’t patient enough.
As for windows, we keep screens on them. He probably wouldn’t fly away on purpose but when a bird gets spooked you never know.
Which bird is it, if I may ask? Just curious.