Because people like to feel needed.
Twoo Wuv shall change him, yes--and that will prove that he needs me, and loves me, and will never leave me. Deep, dark, and brooding? I'm the only one who can bring him out of it, who can help him be more and feel better, which, again, means that he needs me, and loves me, and will never leave me because of all that. Yes, Batman's been through a lot of girls--but if you can manage to be The One...then that's it, you're set for life. You'll always be needed; more than that, you'll always be wanted. And for people who don't mind bending canon a little (or a lot), that's worth putting up with some brooding, or even changing the character so that he can come out of it a bit. Or a lot. I don't know how many people who write this stuff would be willing to put up with it in real life, though.
Part of the reason people write Mary-Sues is because they want to be admired and wanted and needed. It just...doesn't always translate well, for many reasons: messing with canon and thereby throwing people out of the story, not having a main character that other people can relate to (add to that 'overdoing it and making the character ridiculously powerful and unreasonable and flawless'), showcasing the worst parts of modern society (women and men in the media, racism, sexism, etc)...I could go on. But a lot of Suethors are teenagers; they're going through a point in their lives where their bodies are changing, their minds are expanding, and they're often becoming very concerned with what their peers and society think of them. And most people want to be accepted, or admired, or loved, or wanted, or needed, or all of that, and sometimes the only way to be sure of getting that is to write yourself into your stories. I don't know to what extent I've done that myself; my full-blown Sue knew everyone, defeated villains, and gave moderate-to-evil bad guys snarky talking-tos. I'm no psychologist, but I think part of that was wanting to make the canon characters' lives turn out better, part was wanting to tell a dramatic story, and part was that whole pesky wanting-to-be-admired bit sneaking in subconsciously. (She didn't date anyone, if you're curious).
The reason the PPC works is that we're here to point out flaws in writing. We're here to point out how to write better, we're here to analyse bad writing and explain how it could be good. We're not here to stomp on people's daydreams, just...bring them down to earth a little, and teach how to couch them in such a way that they're relateable, enjoyable to read, and (preferably) teach/perpetuate worthwhile values. We're here, in a way, to coach the next generation of writers...if they're prepared to listen to our critiques. And it works because we're writers ourselves, and we've been through bad writing and Mary Sues and a lot of what goes into writing them--and because we understand why we could be better and how we could improve, and we did it. Some of us (a lot of us?) have even gone into Real World jobs that require writing skills or critiquing skills, and I'd like to think we're doing well.
But now it's time for me to stop writing down my deeper thoughts and go to lunch :)
~DawnFire