Your voice is a tool you use to perform and the performance is the art that you can copyright, but if someone sounds like you and can perform better than you, then you don't deserve to shut them down just because they have your same voice. Change the word 'someone' to AI and my views don't change.

If harm--financial or otherwise--is being done, then a machine doing the impersonation versus a person doing the impersonation would make no difference. But I have a feeling you are A-OK with impersonators and just fine if those impersonators get paid for their impersonations.

Your voice isn't copyrighted. Imagine if people who are good impersonators (and make it obvious that they aren't actually the people they're impersonating) get sued for...likeness infringement? Hell no. How is it different if the impersonator is a machine instead of a person? It's not.