I have a cockatiel, who I trust to sit on my shoulder.
My CAG I do not. Although still a baby, her personality is one that tells me that she would use it to her advantage. She is not one that I'd let get the upper hand.
That being said, she tries every day. I tell her no shoulder, but she tries & tries.
Being on the shoulder, they are at eye level and you can't see their body language. My cockatiel has only gotten me twice, and that hurt enough. I can't ever imagine getting bit by a grey.
My big question is: those who allow shoulder-sitters, how do you deal with the poop down your back?