I don't think it's that unsettled, at least not legally. There seems to be precedent for this sort of thing (cf. cases involving Bette Midler or Tom Waits).
I think the hypothetical you create is more or less the same situation as what we have now. The difference is that there maybe isn't a paper trail for Johansson to use in a suit against EvilAI, whereas she'd have OpenAI dead to rights, given their communication history and Altman's moronic "Her" tweet.
> Does Scarlett own her own voice more than Nancy owns hers?
Legally, yes, I believe she does.