Maybe (maybe!) it’s worth it for someone like Johansson to take on the cost of that to vindicate her rights—but it’s certainly not the case for most people.
If your rights can only be defended from massive corporations by bringing lawsuits that cost hundreds of thousands to millions of dollars, then only the wealthy will have those rights.
So maybe she wants new legislative frameworks around these kind of issues to allow people to realistically enforce these rights that nominally exist.
For an example of updating a legislative framework to allow more easily vindicating existing rights, look up “anti-SLAPP legislation”, which many states have passed to make it easier for a defendant of a meritless lawsuit seeking to chill speech to have the lawsuit dismissed. Anti-SLAPP legislation does almost nothing to change the actual rights that a defendant has to speak, but it makes it much more practical for a defendant to actually excercise those rights.
So, the assumption that a call for updated legislation implies that no legal protection currently exists is just a bad assumption that does not apply in this situation.
Her voice alone didn’t get her there — she did. That’s why celebrities are so protective about how their likeness is used: their personal brand is their asset.
There’s established legal precedent on exactly this—even in the case they didn’t train on her likeness, if it can reasonably be suspected by an unknowing observer that she personally has lent her voice to this, she has a strong case. Even OpenAI knew this, or they would not have asked in the first place.
The answer is without legislation you are far more subject to whether a judge feels like changing the law.