Personally, I have nothing against the canonical Harry Potter empire, but I'm hardly a huge fan. I've seen most of the movies on video, and have looked at a few of the books. If Methods of Rationality were just Harry Potter fanfic -- even great fanfic -- then I probably would have no interest in it at all. I don't have time to read half of the published fiction I would like to, and even today, publication on dead trees still tends to screen out some of the worst writing; and published works tend to go through a more thorough reviewing process, allowing the reader to cherrypick the most rewarding reads. Also, I like paper as a medium.
For me, HP and the MOR is not about "Harry Potter," its about the methods of rationality. Actually, that's not quite true. My Harry Potter thinks of himself as Harry James Potter-Evans-Verres. To me, the handsomely-remunerated work by Ms. Rowling may is like the ur-Hamlet. My Harry Potter, in passing, makes useful references to works and ideas that are not widely known, and for that reason, is useful as a pointer and teaching tool.
But that's not really what it's for. The Methods of Rationality is like an anthem or a bugle call or a flag on a battlefield, rallying us wounded and frightened soldiers to re-form our ranks and march forward into the face of the enemy, bayonets forward. The appeal here is not only or even primarily to the intellect -- you can get that through many other sources -- but to the sense of justice and morality and honor and glory. My favorite parts of this work are what TVtropes would call "crowning moments of awesome." So far, the greatest was Harry's frontal attack and local victory over Death itself, in the form of a dementor. (This particular moment first inspired me to draw again, after a gap of I-don't-know-how-many years. I was sad to see the effects of my abandonment of art. At the same time, I gained a new appreciation of people who really know how to draw, beginning with just about any comic book artist.)
There are other moments of glory in the story so far: the first rescue of Lesath Lestrange, bullied by Gryffindors. The launch of the "primitive screwheads" rocket; maybe some others. These moments, conveyed through the medium of fiction -- not argument or even rhetoric -- motivate us to take arms against the sea of troubles that has cursed humanity for so long. We hear the drums and bugle, and we march under the banner of Justice.