If she were a painter, or sculptor and her work won her national acclaim; would her work also be considered 'public domain'?
Just because you win something, doesn't mean that you 'owe' anyone anything. If I win a math contest; I don't owe you a homework assignment. If I win a programming contest, I don't forfeit my software I've written over the years. Why should she be blackmailed (and going national like this is nothing short of blackmail) into giving a very successful TV franchise rights to her personal property?
Not the same thing. Other artists allowed her to use their songs so she could sing them on AI and win.
I'm with you.
She probably paid songwriters big bucks for writing her recent hits. Or maybe she wrote them herself. Regardless, if she has copyrights to those songs, she (and her management) is entitled to make business decisions regarding their use.