Why so sure that it isn't a mating display? Songbirds sing without specific mates in sight. Peacocks will display to humans, or cars, or almost anything. Putting on a sexy show for mates or rivals who might be watching is cheap, so birds do it casually, and it's a reward in itself.

But then, I'm not sure what claim us being made. Is the cockatoo being playful for the sake of exploration? Maybe, maybe not. Does it have unlimited capacity to learn new things and expand its horizons through exploration? No, it's just going to repeat the same things all its ancestors did, transferred into new contexts.