This seems similar to the latest season of Rick and Morty. Whether justified or not in that particular case, it rubs me the wrong way a bit in principle to think that a production can fire someone only to hire someone else to do a near-perfect copy of their likeness. If (as in the OpenAI case) they'd gone further and trained an AI on the impressions of Justin's voice, would that have been considered an AI impersonation of Justin with extra steps?
All of which is to say, this seems like a pretty interesting legal question to me, and potentially broader than just AI.
I don't personally subscribe to the notion that the recent legal invention of intellectual property is a moral right. Capitalism has been doing just fine as a productivity motivator. We don't need to capitalize expression of ideas, let alone pure ideas. I accept the tradeoff of the temporary monopolies of copyright and patent, and I appreciate that trademark and trade secrets disincentivize bad behavior. But I have no desire to try to find new boxes to store new kinds of intellectual property, like Scarlett Johansson's right to monopolize performances of a character in an app that remind people of her performance of a character in a movie. Such a kind of property right is not necessary.