You’re really Hogwarts’ own Severus Snape, aren’t you?
OK, maybe not … but I think Snape does what you seem to think Rowling should do in her books. Despite the fact that Snape is constantly being set up to be the bad guy (by the flow of the story, which you’ve admitted is primarily from Harry’s point of view), we see that he is not. Now, what will happen in the next three books is anyone’s guess, but so far, in Snape, we have the author’s acknowledgement that, yes, someone who is rational, intelligent, and indeed, trustworthy enough to have earned Dumbledore’s respect can still not like Harry.
In fact, Snape’s objections to Harry are your own. He believes that Harry generally believes himself to be above the “riff-raff”, having led a life of privilege, including being favored by teachers. We, the readers, see that Harry’s wealth and fame actually contribute little to his ability (as another poster observed, mostly by dumb luck) to extricate himself from the situations into which he is thrust.
It seems to me that the root of your objection is that Harry is different from the traditional children’s literature protagonist, in that he has advantages. So he’s different – how is that bad? He’s unique, original, and maybe – just maybe – he appeals to a generation of kids who are advantaged compared to much of the world, and yet they still find themselves having crises of identity. This is Harry in a nutshell, IMHO: “I am advantaged, this world is not a level playing field, and to most of the rest of the world, I seem to be ahead of the game. Why, then, do I still have insecurities and problems and challenges to face?”
Life is not fair. People of ALL sorts have problems, and to downplay the problems of a wealthy, admired young boy – just because his problems are not the problems of the protagonists of favorite children’s books of your youth – is unfair both to the character and to the author who saw fit to create a unique character.
Harry’s popularity indicates not only well-plotted, intriguing books, but IMHO also is indication that children (and adults) identify with him.