If Jackman’s paycheck is smaller, then 20th Century Fox can spend some of the money that was originally allocated for him on the production’s budget instead, which then means that Jackman, Mangold and the rest of the cast and crew have more freedom to make the movie the way they want to rather than create a watered-down version.
Why would that be helpful?
Well, by making Logan an R-rated blockbuster, that means not as many younger moviegoers will be able to see it in theaters, which subsequently means that it’s likelier to make less money (though not guaranteed, as evidenced by Deadpool’s success).