I've read and enjoyed several Harry Potter fanfics. Well, actually -- in many of my favorites, he isn't Harry Potter. In "The Accidental Animagus" he's been adopted by the Graingers (and Hermione is his step-sister), in "Harry Potter and the Invincible Techno-Mage" (a rather one-sided "take that" which is redeemed mostly by the spectacle of various Marvel Universe characters demonstrating what real magic looks like) the Dursleys won their long-awaited Darwin Award whilst touring a factory in America and Harry ends up adopted by Tony Stark, and of course in "Harry Potter and the Methods of Rationality" he is Harry Potter-Evans-Verres (and his adopted father is a scientist).
Which almost gives away why; in each case, the focal characters (often Harry, as often Hermione, rather rarely Ron which seems a bit unfair to me!) are a little more logical, are inclined to look at things rationally, analyze instead of react emotionally. And they also generally have more confidence in themselves than the original cast did.
And this leads me to understand better the story J.K. Rowling created. Harry is, bluntly, a bit of a slacker. He doesn't have any great dreams or wishes; he came out of a background of neglect that leaves him wanting mostly enough to eat and a warm bed, and a certain impossible longing to turn back the clock and have his childhood over again with the parents he never knew. The magical world is strange and scary to him, and there are certainly enough challenges (classmates who either don't understand him or are actively antagonistic, sadistic teachers -- well, mostly teacher -- and of course the threat of Voldemort. That's got to be tough; being only eleven and learned the greatest dark wizard of the age has gotten it into his head that he needs to hunt you down and kill you.)
But Harry is basically reactive for most of the books. The only thing that actually excites his interest is playing Quiddich, and even then he seems to mostly hope that by doing what the coach says it will all somehow turn out right. He is more than Oliver Twist here; he's practically Candide, convinced that all will turn out for the best.
But open the focus for a moment. His major guide to the over-arching plot is Dumbledore. Dumbledore originally comes on in full Ben Kenobi/Gandalf/Merlin mode; the wise elder. Unlike many of those he waits until the beginning of the final act to kick it, though. Thing is, it is progressively revealed through the stories that Dumbledore is holding back, that he is hiding information, and that his plans are not anywhere near as tight as he might have hoped. Indeed, the final revelation is basically that Dumbledore knows Harry must die to stop Voldemort, and has been working all his plotting to keep Harry unaware of it until it happens. Apparently it never occurs to him to try to find a better solution.
So, sure, it is fun in so many fanfics to snark at this; to show a Harry who thinks a little and asks the questions he really should have asked, and to have people who confront Dumbledore on some of his more inane moments (leaving Harry with the Dursleys, for one, but the entire underplot of "Philosopher's Stone" is a truly insane gambit.) And the magical world has flaws that deserve a few pointing fingers. The wizard prison of Azkaban, for instance, makes Guantanamo seem practically righteous.
But the original tales are in that one way a much realer world. The kind of world of fog of war, of rationalization instead of rational behavior, of people who aren't aware of THE PLOT as a giant puzzle to be solved but instead are just taking each day as it comes and reacting to each challenge as it becomes finally clear.
To paraphrase; winning the battle against Voldemort is something that happens while you were making other plans.