I saw that Robin Williams setup a deed to prevent his image or likeness being used for film or publicity that covers a period of up to 25 years after his death.
Long-lasting transferable exclusive rights that will inevitably end up being owned by corporations could also be a problem, though, particularly when the lawyers are motivated to interpret them as broadly as possible so that it becomes dangerous to even slightly resemble anyone famous who died less than 70 years ago unless you have paid various licence fees. So I'm not sure it's worth giving up our current freedoms just to avoid some distasteful crap on the internet which I can easily avoid.
However, there might be a way of doing it that doesn't create a new category of intellectual property. I think I read about a case that went a bit like this. Parliament created some kind of privacy right. A newspaper asked someone for permission to publish some pictures that could be an invasion of some person's privacy. The person asked for money. The newspaper went ahead and published without permission. The person sued. The newspaper argued in court that if the person was willing to let the pictures be published in return for money then they didn't really care about their privacy. The judge said: it does not seem that the purpose of the legislation was to create a new category of intellectual property so that argument might be valid... I've garbled the details and I'm not sure of the final result but that line of reasoning is interesting, I think.
https://www.theguardian.com/film/2015/mar/31/robin-williams-...
I don't know if it could be extended further, but I feel like there is merit for it to be considered in this case.
In Denmark people own the copyright to their own voice, imagery and likeness:
https://www.theguardian.com/technology/2025/jun/27/deepfakes...
I think that it is probably the right way to go.