Again just b/c you think it doesn’t look like Jack, doesn’t mean that they didn’t get the likeness rights. Just like how Star Ace infinitely misses the mark on their figures and headsculpts even though they have the likeness rights to the licenses they’re producing. Same could be said with many of Sideshow's 1/6 figures and statues for that matter. Heck, there are even a good number of times HT misses on the likeness no matter how realistic their portraits are. HT 1/4 TDK Joker barely resembles Heath Ledger if at all depending on who you ask; yet, it was still made with Ledger's likeness rights regardless of anyone's opinion on the accuracy of the sculpt.
Also, you saying "It's the sculptors own interpretation of his likeness is all" is pretty much what every sculptor does. Unless you're Sideshow that is (who blatantly said that their Clint Eastwood headsculpts are 10% caricature), most sculptors interpret the likeness of the actor to the best of their ability at the scale they're working in. This is why nearly every time a new sculptor tackles a certain actor/character that has been done before (like TDK Joker or Indiana Jones for instance), they all look a little different rather than carbon copies of each other. Inigo himself has had at least 4 versions of Indy if not more all looking a little different from the previous version. Same with Dean Tolliver and all his different TDK Joker sculpts.
Sure, the Beast Kingdom figures don’t look good; but, it isn’t the first time and won’t be the last time a figure comes out that doesn’t look like the actor it’s supposed to be portraying. Your personal feelings on the accuracy of the sculpts for those Nicholson or Keaton figures has no bearing on the fact that they got the rights to their likenesses to produce the figures.