I liked Fight Club as a movie. Attaching any further purpose than that is like ??? seriously.
Fight Club combines every juvenile male fantasy I care to list all into one. Excelling at traditional violent masculinity, being Robin Hood, being Brad Pitt,
secretly being capable of or living out said fantasies.
Just the idea that not only would an individual be able to be a "moral" compass for a world that generally seems stacked in favor of the already privileged (never mind that the people who like this are crackers) but that even their extreme apparently insane efforts to impart morality and more egalitarian standards to the world (if not moral) meet with success.
As it stands, Tyler Durden doesn't... "eliminate the fractures to his psyche" as some sort of penance for his own crimes, but instead he claims the fruits and self-determination of his amoral counterpart. The psyche doesn't mend because he shoots himself in the head or because he repents, it mends because he decides that being an insane terrorist is something he wants to control rather than be controlled by.