"I don't have much to gain from hanging out with Hagrid" and "I don't care about Hagrid's well-being" are radically different statements, and the former doesn't imply the latter.
But what if he's wrong about the former? It seems to me that Harry's biases have led him to a false conclusion. It's true that Hagrid is not terribly smart, which is I gather what causes Harry to write him off -- but Harry has not bothered to find out about Hagrid's other abilities before he made this judgment.
I mean, firstly, as a half-giant, Hagrid is highly resistant to magic, which is an ability of exceptional flexibility in this world. Secondly, Hagrid has unfettered access to the Forbidden Forest and all kinds of interesting alliances with the creatures who live there--is Harry entirely sure that he will never have a use for a juvenile dragon, a pet hippogriff, or an army of spiders? And thirdly and probably most importantly, Hagrid has access to rare magical components (e.g. unicorn hair) that Harry could use in spells or potions, potentially giving Harry access to a wide range of new skills and abilities. I think he made a very unwise decision when he wrote off Hagrid.
Yes, this is a failing on Harry's part. Harry doesn't realize how useful things can be that aren't connected to sheer brainpower. Harry is not a perfect individual. He's very far from it. If Harry had gone and befriended Hagrid that would make him a less plausible, more Mary Sueish character.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: