The war delivered some new information, but it contributed nothing to the final battle. Think of the war like the chunin exam in part one. It was interesting, introduced new characters and fleshed out some we already knew and gave pacing to the story. Or even the Save Sasuke arc. (Although the save sasuke arc was more vital to the story than the war arc because all those mini-fights allowed Naruto to continue on to the bigger, over-arching goal of saving Sasuke.)
In the end, Naruto and Sasuke still had a brawl. The powerups, the mass casualities, the death of Neji and Asuma, the words of Itachi and the Hokages — none of it contributed to their understanding of each other, or assisted them in reaching any kind of peace.
In the end, Naruto and Sasuke had a bare knuckled schoolyard brawl, and only when Naruto beat Sasuke did he finally relent.
The over arching story was their fight and Sasuke's redemption. It carried over all the other arcs. But instead of weaving the war arc into the storyline, it's just a bubble. Once it was over, then they could fight.
There was no thought to collateral damage, no deeper understanding of themselves and each other. Just a fight.
Would Naruto still have saved Sasuke if the war hadn't happened? Yes. There is no doubt.
I'm not saying the war arc wasn't an big facet of the story. It was and it filled in a lot. But it is no more important than the chunin exam was to part 1. The overarching drama of Sasuke's redemption did not hinge on the chunin exams, no more than his redemption hinged on the outcome of the war.
Yes, the war would have happened, espeically for the reasons you mentioned. It was foreshadowed early on, so it was always destined to happen. But if it didn't, Sasuke would still have been redeemed some other way. In the end, the outcome didn't directly contribute to Sasuke's redemption, and Sasuke's redemption would not have impacted anyone other than Naruto.
And in the very last pages, we discover that Naruto and Sasuke STILL haven't buried the hatchet!! So what was the point of the story if not to materially change the two? But it didn't.
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I could write a lot more about how the story went wrong, where Sasuke's redemption arc split off from the rest of the story and never rejoined it, and how series' like Harry Potter follow the main character's arc alone, with every incident and circumstance included in the book because it points to the culmination of Harry's story. (If we were to view Harry's story through Parvati Patil's pov, it would be full of holes and unknowns leading to his success. In short, it wouldn't be his story.)
Naruto has long been suffering because at some point Kishimoto confused it with Sasuke's story. And then in the end with Hinata's story. All the events in the Naruto universe that are going on around him are definitely part of what makes up his world, but they are not all important in telling Naruto's story.
That's what I mean by the war not being central to the story. It was filler, meant to pace out the end of the series, like the chunin exam did in the beginning. The story of Sasuke's redemption — which replaced Naruto's story of protecting the village, getting the girl and becoming the leader — only picked up again after the war was over. Not because of it.
Your comparison to HP is apt. Things happen around Harry, but the story consistently remains focused on his inevitable clash with Voldemort. Along the way, Naruto stopped being about Naruto's quest to become Hokage, gain respect, and get the girl. It became a story about Sasuke's redemption and the history of the Uchiha. That's why the war arc mattered, I guess.
Persona 5 hype 
