If AI can be so convincing, then your publisher won't we wanting to pay you to make any new songs if they can just pay an AI guy for a few days to crank out a new song.
I think a person or artist should own their voice, but what is the threshold for an altered ones that is different? And for 'real' human voices someone can sing and sound just like you, that's not a crime. Would it be the same for an ai-generated voice, anyone can copy any of them?
With the troubling to me decision that you can't copyright ai generated images, it feels natural to me that you could probably not copyright / control ai generated voices the same way. This is a mess, then I could take my ai generated video and voices of presidential candidates, politicians and they can't stop me maybe, because it's all got that magic adjective "ai" in front of it.
Record companies can make money off of it -- so they will support this in some way. And they will fight to make sure people can't easily do it on their own systems (which is the way it's going right now).