This was approached all wrong. The first highly publicized demos of singing generated like this should have been of dead people - Michael Jackson, John Lennon, Elvis. First, it's not clear who has the right to sue, and in what jurisdiction. Rights associated with those people have been transferred and resold enough times that there's no clear claimant. Second, many people have impersonated those voices, so there's a…
The courts or the legislature are going to have to address how your rights to your own image being synthesized like this, but again, I have no problem with someone retaining the same sorts of original ownership rights when it comes to derivative works that use data collected from them, beyond just who owns the copyright to the works in the dataset. (voice, video, images, etc.)