This question of "Gryffindor versus Slytherin" raises many, many new questions and sets up several of the conflicts that are to come later in the series.

Such as:
Sterotypes --- "The world is not divided into good people and Death Eaters"

Choices influencing magic --- everything is not predetermined

Harry's origins and connection with Dark Wizards. --- Voldemort, the Black Family, Salazar Slytherin, and finally the Peverells.

Harry hasn't a clue about what he'll be facing, but Dumbledore (and Jo) know that growing up is hard enough without having a firm foundation of solid principles such as this one. He will be pulled in every direction, provided with every form of distraction to keep him from destroying the Dark Lord. How is he to withstand and counter all of those influences without the wisdom that his fate is not pre-determined, and no other person can decide for him what that fate will ultimately be.

I think a big part of Harry finally determining that he is a true Gryffindor leads some of his actions in the following books. In PS/SS, Harry goes after the Stone because he is frightened, deep down, of a returned Voldemort (and, as we've discussed, he might have been led there by Dumbledore; personally, I think this theory is a bit far fetched, but I guess it is plausible). In this book, he goes down to the Chamber to rescue his best friend's sister.In the first two books, Harry determines to himself at one point that he won't interfere anymore, that he has nothing to do with the situation; that is, until something tips him over the edge and he feels like the only one that can do something. But in PoA,why does he sneak into Hogsmeade? Why does he insist they go down to Hagrid's? Why does he sprint after Ron and Scabbers? Why does he launch himself at Sirius? He starts to accept the fact that he is a true Gryffindor, and in true Gryffindor fashion, he stops thinking everything through and goes on impulse. It's not always a bad thing, but it is the beginning of Harry acting first and thinking later (unless Hermione tries to persuade him otherwise, which happens less and less as the series goes on).
I also think it's a good connection to Harry's parents, especially his father. James was the epitome of a Gryffindor, and Harry finds James inside of himself in PoA. It could also be linked to the parallel book theory, and HBP. In CoS, Harry determines that his choice of house is what seperates him from Voldemort. In HBP, he determines that his choice in regards to the prophecy, his life, and his destiny are different from Voldemort's. Harry will have to make many difficult choices in the future. He will be pressured and pulled towards the dark inside of him. And yet, he chooses the light, the hard but right path, and through those choices, he will choose what he becomes.

The theme of questioning his Sorting is important for two very good reasons. One, it implicitly states that it's our choices that matter first and foremost. What this establishes is the question of choice vs destiny. He could march off to his death later, but doing so willingly is what matters.

More importantly, though, I'd argue is that it establishes Harry's fear of not fitting in more strongly. By establishing that he does, indeed, fit in this early- it gives him something to fight for. If he doubted the entire time that he belonged in the wizarding world, would he be willing to die for everyone? Sure, he'd died for Hermione, Ron, et al. But to fight for the rest of the world after everything they say about him? Eh.

Instead, it establishes a place for him. And more importantly, he learns that his choices are what earned him his place. With the Dursleys, he couldn't so much as question and was punished for things he'd done inadvertently, let alone his deliberate and often rebellious actions. In the wizarding world, he is valued for his actions and becomes a hero- for being a rebel.

(Also, if he'd been killed earlier in the books, whether by the basilisk or Lucius, etc.- would Voldemort's soul piece then take over his body and bring him back earlier?)