Unfortunately, the law is already quite stupid around this.

There have been many cases where a company wanted to hire say, actor X to voice their commercial, actor refused, so they hired someone else with a nearly identical voice, the original actor sued and won(!!!!!) because apparently it's their "signature" voice.

I disagree because obviously that means the other person has no right to make money using their voice now, at no fault of their own?

But yeah I'd imagine you'd have the same problem here - you can't generate a picture of say, Brad Pitt even if you say well actually this isn't Brad Pitt, it's just a person who happens to look exactly like him(which is obviously entirely possible and could happen).