Copyright might not be needed. SAG created a rule after Crispin Glover’s face was used without permission via a prosthetic in Back to the Future 2 to ensure it

Copyright might not be needed. SAG created a rule after Crispin Glover’s face was used without permission via a prosthetic in Back to the Future 2 to ensure it never happened again. I could easily see a similar rule being added by an appropriate union to their contracts to prevent AI copies of voices that weren’t approved by the original actor.