I disagree on Buffy Summers though. While never in the top tier of the characters I liked on her own show, she very quickly stood out as a little more than just the bland main character. Her tangle with certain death in "Prophecy Girl", her emotional roller-coasters in seasons 2-3, her losing her mother and becoming a surrogate one for Dawn in season 5 and – most importantly in this context – becoming a General, a Leader in the seventh season, these things brought her up above the typical blandness. Especially, as I said, the latter. Her was a revived hero who wished she was still dead, who thought ill of her friends for bringing her back, and who, at the same time, grew into a role not as the hero, but as the general. The general being the one making the tough decisions – often the horrid decisions – that needs to be made to _win_. That's not typical of a main character. (Just compare to earlier seasons of the very same show, where these choices were always left to Giles to make for her) It's dark, it's complicated, and it is engaging. And I can't think of Buffy Summers without thinking of her entire development, season 7 included, and thus, she doesn't really fit the category of bland heroes.

But that's a long digression. My point is I agree with you. I usually root for the villain, or the manipulative mentor, or even the skilled, overlooked sidekick. Rarely the hero. The times I do root for the hero is when (sh)he has attributes the heroes rarely have – like Buffy in season 7, or for that matter, the increasingly confused Paul Ballard on Dollhouse.

Or Batman. Like you, I'm a Batman over Superman-guy, easily. Batman is, in fact, my favourite super-hero of all time, and I love every single story where they elevate the reason why: His will-power. The gadgets are symptomatic of his stubborn insistence on always being prepared, always having figured out every possible angle, always having a plan ready. His martial skills are a result of his years of training – a result of his renewed decision, every single day for two decades, to keep shaping himself until he fit with his plans. His deductive detective skills are obviously aided by his vast intellect, but usually root in a simple rejection of defeat. Batman never, ever gives up, and thus he'll stay at a mystery until he figures it out.
In short? Batman's a super-hero because he's insanely, unbelievably stubborn. He made a plan at eight years of age, and his every single action since that day is about performing that plan in the mos efficient ways he can think of.

That's usually a description of a demented villain, or at best, a mysterious old mentor-character that aids the more accessible, more relatable, more bland hero. Batman's super-power is basically obsession. That makes him interesting, that makes him more than a bland hero like Superman or Harry Potter or Jack Shepard. So while I agree with your general point, I think there already are heroes like you're requesting, they're just few and far between.

And again, just so that's said – on Harry Potter, I could not agree more. In fact, I agree so much that I've been unable to talk myself into reading another novel in the series since "Goblet of Fire" first came out, and only watched up to date on the movies this summer.