I really don’t think that forcing cockatoos into independence before they’re ready is wise. They are, after all, highly social animals who bond for life in the wild. It is a very healthy thing for this bird to have formed a bond and he’s just not ready to accept the concept of independence yet. I would try and make him certain that he finally belongs and that when mommy and daddy leave they’re just doing all the things he’s been doing too.
I think after a while Bianca was so tired of being taken places that she took being left home alone as a relief.
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The issue with this is #1 they've had their U2 for 2 years already, so this is not a bird that is new to their home, to them, or to their daily schedules and routines. So his screaming whenever the wife is not with him/he can't see her has only gotten worse and worse over the entire 2 years that they've had him, she's "his person" and this is to be expected with a U2 who bonds-closely with one particular person, however after 2 years this would not be "forcing him into independence" at all, but rather helping him get over his severe separation-anxiety and feeling of insecurity and anxiety when she isn't in his view/with him.
You mentioned that "it's not healthy for the Cockatoo to be forced into independence", even after 2 years of living with his Flock and bonding-closely with "his person", but how is it healthy for him to still be screaming literally 24/7, 365 if she isn't with him?
If this U2 has been displaying this separation-anxiety every time she leaves his sight for 2 years, then that ALSO MEANS that in-addition to he and his wife losing their minds, this U2 has ALSO been constantly feeling anxiety, stress, insecurity, etc., hasn't been getting a solid 10-12 hours of sleep every night, and has been bored to tears (by his own-doing) because he's not doing anything at all to stimulate his mind or his body because he only thinks about where his person is 24/7...FOR THE LAST 2-YEARS!!!
There is no way that them continuing to try to appease their U2 by constantly making sure she is with him after 2 years of doing it is at all healthy for this bird, not in any way!! Not physically, mentally, emotionally, psychologically, or behaviorally healthy for him! If they had only had him for a few months then this would be a different story, but even then you still need to start GRADUALLY teaching all parrots who have separation-anxiety at this level that they can be alone without their person and have fun entertaining themselves while they are away, and eventually get them to trust that their person is going to always come back, which is a lot of the reason they start to scream like this when they first bond to someone closely, especially a re-homed bird. So it's absolutely much, much healthier for them to start to teach him that he can feel secure, happy, and have fun by himself, and that his person is always going to come back to him, and it's okay if she isn't always with him 24/7.