Someone's vocal characteristics are not meaningfully creative; it's the intellectual content of a work and specific instance of a performance of an artist's skill in singing or writing or drawing or fabricating that content, that makes the result copyrightable. Therefore, it seems like it's a stretch to think voice-mimicking AI works might be copyrightable by the mimicked artists.
You can't sue someone for mimicking someone else's voice well enough to be confused for the mimicked creator's voice. Some people can do some voices quite well. AI can just do it better, faster.
I hope the courts put a swift end to this, but maybe they'll try to uphold the status quo—entertainment megacorps get what they want—and only reverse course after a few years when it becomes clear that everyone's mimicking everyone else's voices and pictures for fun and profit and any attempt to maintain copyright or any other IP protection on such mimicry is absurd.