If Neji's death made him question himself, Hinata's death would destroy his view of reality completely. Now, regardless if you ship them or not, you must accept that they have a lot of influence on each other. Hinata was someone who applies Naruto's ideals. In fact, she's the one who does it the most by far. What in the world do you think it'd do to Naruto emotionally if Hinata was killed in order to save him again?
In fact, the answer to your question would be it's a good thing Hinata didn't die because it'd be just repeating something that's already happened. Pain arc remember?