It's essentially the performance of a composition vs the composition question again: at what point am I mimicking someone to the extent they have a valid claim on a portion of my work?
I expect it'll enter the courts a few milliseconds after someone clones a dead actor (without their estate's permission) for a new performance.
There's always been an inherent tension in the US distinction between a law of nature and a creative work though. It seems a bit silly for me to claim patent / trademark on a vector that encodes my likeness.