From some one from the old schol who has been righting fan fiction for... well lets just say early 90's and leave it there.
Mary sue is actual a "newer-slang" term, we used to call it "Author Insertion" stories. Some can be very good if they keep into the context of the world, and not Brake the rules of the world. "Ie show up as a god, slay the series villian, render 50 volumes of manga mute, and 200 episodes useless.
Some good, some bad. I like the well written ones my self. But then thats me. For every Good bit of fan fiction theres 50 bad ones.
A way to see it is the author puts some of them selves into it and have allowed you to peek into their fantasy if you wish, you may even share the same fantasy. Its definitely not for everyone, and I have actually written standard Fan Fiction, Author insertion, and Cross over ones. So i been there done that, and like its been said before Fan fiction isn't for everyone. (no i haven't written PS fan fiction... yet)