Not just cockatoos, but also magpies, at least that's what I've observed recently. Both are intelligent birds with not so good reputation, I'd avoid making them my enemies. Both can do significant damanages to your garden and plants. Cockatoos and magpies are intelligent enough to observe human beahviour and retaliate when those who try to offend them when they are not present at home (don't ask me how I know this...). Over time, I learned to make friends with them, make the gardens friendly and attractive to them, toys (river stones, small toys, ablone shells, etc.), clean water source and so on, I've been living with both cockatoos and magpies for years now. It seems that the magpies have a strong sense of territory, the same group returns everyday, while cockatoos visit less often, or simply randomly.
On cockatoos: One of my neighbours have been keeping a white cockatoo as pets for 10+ years, the bird start to lose feather on tis chest... The bird is kept in a large cage with a meshed window facing a park / playground, the bird says hello to pretty much everyone who waves at or greets it. Sometimes it even says "have fun" in a weird tone - it took me at least 20 times before I figured out what it was trying to say ;-)
On magpies: their beaks are not at advantage to open bin lids as cockatoos'. However, individual magpies are smart and powerful enough to open overflowed bins' lids and mess up the garbage.