I'd say that the extent to which even use of a AI as a tool might affect copyright still needs to be tested in court. It's already been ruled that you can't simply have an AI write all possible melodies over a weekend and claim that your human input is selecting all of them and copyrighting them all. So simple selection may not be enough but what sort of additions, assemblage or whatever is required remains to be seen. These are uncharted waters and the law on the use of randomness or algorithmic composition is mixed
Agreed, it needs to be tested in courts, but I don't think there's anybody who knows how to do that yet. Legal experts better hurry up, it's happening now.
The melody and lyrics are the elements that are protected by copyright. Although you can copyright either separately. You can register the copyright with sheet music. I doubt anybody could tell by looking at the sheet music how it was created. And what's not to say that given a sheet of music that someone plays or sings in their head is not enough to participate in the copyright? The may make an artistic change to it, phrasing, note choice, lyric change.
AI does have the benefit of scanning all existing copyrights to be sure the song is original.