On the deeper level it’s the difference between the series being a morality play and a tragedy. In a morality play the main character learns and grows and screws up and learns some more and suffers and learns but in the end triumphs over evil thanks to what he learned. In a tragedy you do everything possible to make the readers love the main character then you kill him, often times pointlessly. If Harry dies in the end, especially if he dies without striking down Voldemort, the whole thing becomes a tragedy, and the moral lessons become somewhat weakened (what’s really the point of all that learning and growing just to bye the farm).
Tragedies tend to be less popular because we like our heroes to triumph, and there is a certain cruelty in spending hundreds of pages making people love a character just to whack him. It would have been kind of funny after 10 years of selling vast forests of books to turn the whole series into shaggiest dog of a tragedy ever, probably would have made some of the literary nerds like the series better. But I think it probably would have irritated a lot of the audience.
I wasn’t going to even buy the book or see the rest of the movies if Harry died. It would (to me, and to my children)become pointless.
I think that Harry’s death would be sad, but it wouldn’t be tragic. It would have been following a tried and true formula called The Hero’s Journey. It would have been an interesting twist on the formula to have Harry’s death be the actual final triumph. J.K. Rowlings pointed out again and again in the book (and in the series) that death isn’t always a tragedy. It’s sad for the living, but I wouldn’t say that Harry dying, really dying, and killing Voldemort in the process would be tragic (heroic more likely).
BTW, literary geeks aren’t turned on by either a classic tragedy or a classic hero’s journey; they’d probably salivate at no resolution ala black screen on the Sopranos.