I cover Talon up at night, and she sleeps in my room where I can be quite noisy at times. She does fine.
SHe does have a sleep hut that she LOVES!!
I think like us, they like the security that a little privacy can give you. It's a comfort to feel safe when you sleep, and being out in the open to me, is not comforting. I use a large navy blue sheet that I leave a little opening on the sides, so she still has some light if needed.
I would try covering her, but do so gently at first. I never take the cover completely off, I just lift the top up onto the top of her cage, and at night after she is in her cage, gently lower it down as I am talking to her and telling her Good night!
It will take some adjusting on her part as well if she is not used to being covered.