But is that true? If I were a gifted mimic, I couldn't go out and make a song called "Sad in Toronto", even if I was very clear about not actually being Drake?
The op is extremely certain that they have interpreted this law correctly, but the fact of the matter is that a case like the one you describe has never gone through US courts, so we do not know. We are likely to have a court case sometime in the next few years it seems, who knows how long it'll take to get an answer though.
There was a very important and similar case though where Bette Midler sued Ford over inappropriate use of "her" voice performed by an impersonator.
The context seems important in that case though. Ford had the impersonator sing a song that she herself released! (They had acquired copyright release for that part) So there's no reasonable claim that Bette Midler was not the one they were impersonating.
If you sang a song you wrote in a voice extremely similar to Drake's without mentioning Drake in any way, then that seems very different to me.
A gifted mimic is not a mechanical reproduction. The right of publicity doesn’t protect you from people with similar appearances or voices, it does protect (to a certain extent) against uses of mechanical reproduction of your appearance or voice.
Because it is separate from copyright, US federal statutory fair use considerations don’t apply to this right (I’m not sure to what extent Constitutional fair use might apply to it; statutory fair use in copyright largely recapitulates what were found to be Constitutional limits on the copyright power stemming from the First Amendment, I don’t know if it has ever been considered the extent to which the First Amendment, applied ot the states through the 14th, applies similar restriction on the right of publicity, which is in the US, to the extent it exists, a state-law intellectual property right.)
There was a very important and similar case though where Bette Midler sued Ford over inappropriate use of "her" voice performed by an impersonator.
https://en.m.wikipedia.org/wiki/Midler_v._Ford_Motor_Co.
The context seems important in that case though. Ford had the impersonator sing a song that she herself released! (They had acquired copyright release for that part) So there's no reasonable claim that Bette Midler was not the one they were impersonating.
If you sang a song you wrote in a voice extremely similar to Drake's without mentioning Drake in any way, then that seems very different to me.