There have been a couple cases or so in the US where singers have sued over their voices being imitated in commercials. As far as I know none of their copyright claims succeeded, but some still won on other grounds, such as the common law notion of appropriation of identity, or California's laws of publicity rights and federal laws on false endorsement.

As I said, they lost on copyright claims but these cases involved their natural voice. If the voice was a made up voice, such as a character an animated character, I wouldn't immediately dismiss the idea that it might be copyrightable.

Some of these people get paid for voiceover work, so this could get interesting

yup, I would stay as far as possible from using this wit explicit permission, just putting it out there, the project has created legal risk IMO.

At least in the US, you can’t copyright your voice. Publicity rights is a can of worms depending on the jurisdiction.

Tangentially related, if you have your voice print as a security mechanism at a financial institution (Vanguard), you should ask them to turn that off.

The Australian Taxation Office uses a voiceprinting system when you phone them, and I'm not sure there's a way to opt out.