I’m not even sure it is greed, the end of JW4 set up the next film - Caine vs Akira. A cat-and-mouse chase across continents with her fired up by vengeance and him reluctant to fight her because he knows is right in her own way. Then Anita involved Caine’s daughter, precipitating the final showdown in which Akira realises she has become just as bad as Caine and backs off from the killing blow. At which point Caine strikes and she is forced to fight or die. The winner (likely Akira) gets to lead the franchise for the next few films, probably wracked with guilt, walking the Earth like Caine (the other one) perhaps hoping to do enough good deeds to.assuage their guilt.