Mesaana is not dead, she is alive in the Tower with the mind of a child. Do you think that by keeping her alive in this state, she is denying the DO access to her, and denying his ability to reincarnate her? (albeit unknowingly, on Egwene's part)

Or, do you think that, since Mesaana's mind is broken, even if she were to die she would be no use to the DO anymore?