There is no way to exactly fingerprint a voice. There isn't a mathematical definition of a voice. Even fingerprints and DNA aren't completely unique; think of twins. This means that a subjective judgement would have to be made when deciding ownership.
Look, I'm obviously not going to convince you. But I hope, for your sake, that this legal framework doesn't come to exist because you will not be the winner. Disney, Warner Brothers, or some other entity with deep pockets will own just about everything because they have the lawyers and money to litigate it.
There are real problems and dangers of trying to turn everything that has value into capital for capital owners.
Yes, that was the distinction I was trying to make. These cases are fact dependent. I'm willing to admit that in this specific case there might have been both the intent to imply endorsement by a specific person and that practical result.
But as you can see in the other comments where I'm getting reamed, owning a voice outright is a pretty popular (if currently legally dubious/impossible) concept.