To an extent, I agree; however, two quasi-defenses:

1: It does actually get less Mary Sue-ish as time goes on; a large part of the purpose of the starting chapters is to establish Harry as a rationalist badass, and once that's been established that element of his character becomes less prominent- see, eg chapters 10, 18, 30-31, the whole Azkaban story arc, and probably a few more.

2: A major purpose of the story is to be awesome/to show a rationalist being awesome. (Also, it's explicitly influenced by another story often accused of Mary Sue-ish ness, Shinji and WH40K.) If it didn't skirt close enough to the edge of Mary Suedom to be perceived as an outright Mary Sue by some, it wouldn't achieve its goals.