Story wise, it only comes into play for part of Lin's story, otherwise it is jut there for fun, and as a way to build up submission points, if you want to have a high score for it. Certain events do require certain things to be above a certain level, but I don't think submission is one of those triggers (though I am possibly wrong there).I have searched a couple times trying to avoid spoilers so I will just ask. Is the dungeon important for story? It's really not my thing but outside of Lin I think I have completed all the story for all the other women I believe.