That's a really good question. I suspect most authors don't create book covers with pictures of famous actors because of photographer copyright. Stock photo sites with celeb photos usually license them only for editorial use only (so book covers are out, since books are products being offered for sale). I've been using Shutterstock for years and have never come across a celeb photo that wasn't tagged editorial use only. I suspect that may in some cases be because commercial uses might involve making it look as if the celeb endorsed a product he or she didn't endorse, and that would create legal complication for the company licensing the photo as well the person using it. Even the model-released photos can't be used in certain kinds of product ads, though I forget what the exact restrictions are.
What about if the likeness is not based on a specific image? Like, say I hire a cover artist to do a piece of original art and say, "Make the character look like Benedict Cumberbatch" (I'm using him as an example because he has a very distinctive look), and the artist is skilled enough to do it. Would that cross the line?
And now I thought of a parallel in audiobook form. Larry Correia has a character in his book Monster Hunter Alpha who sounds exactly like Christopher Walken. And it's not some coincidental regional accent thing. It's where the author said, "Can you make this character sound like Christopher Walken," and the narrator was like, "Yeah, I've got a great Christopher Walken impression ready to go." And obviously that hasn't caused any problems. You'd think that original cover art that was made to look like a celebrity would fall into that same category, yet I can't think of a single cover I've ever seen where an original character blatantly looked exactly like a celebrity in the original art on the cover.
I wouldn't assume anything about that. Best to get an actual legal opinion on it or avoid the issue altogether. As was mentioned before, Shepard Fairey got into legal trouble when he based the Obama Hope poster on a photograph owned by the Associated Press. They settled out of court, but the judge urged a settlement and said Fairey would lose. The fair use defense didn't protect him, so I wouldn't risk that on a book.
Looking at that link you posted, looks like settling meant he had to share profits on that image with the AP and do a series of similar images for them, so it's not even as if he got to do one easy thing and then keep getting all the profits from the image. It wasn't a "can I just pay a fee and then keep doing what I was doing?" situation.