Notice it's not "Famous person vs Non famous person". It's "Famous person vs Corporation". And in those cases it was not about the voice alone, but the use of it (which was found to be intentionally soundalike and misleading).
A lot of people look handsome, sound handsome and are even stylish. So some rich person can randomly claim some one looks closer or sounds closer to them and hence needs to forced to wear a mask to prevented from even talking?
So what happens next, when AI bots begin to sing, compose music, teach, paint or anything for that matter?
I don't think it's a trivial thing as vanity though it would be a convenient culprit. Instead, I believe what makes more sense is endorsement and one's right to their likeness. If the person had merely sounded similar it probably wouldn't be an issue. Rather it seems to be that in each case the party caught out seems to have intentionally sought to convince people that she endorsed the product and/or may have been financially tied.
This isn't true. At least with respect to "soundalike" see, e.g., Waits v. Frito-Lay 978 F.2d 1093 and Midler v. Ford Motor Co. 849 F.2d 460.