I don't like the way Neji's death was handled either. It did seem like more of a showcase for Naruhina and also Obito's fascination with Naruto and why winning Naruto over was important to him. Don't get me wrong I am a Naruhina fan, but that was the wrong time for that.
Neji spent his whole life resenting and rebelling against his fate to a point where he meant to harm Hinata until he finally realized that your fate is your own to make and not something you are locked into. Naruto told Neji after the chunin exams that the fact the branch family has to sacrifice their lives for the main family has to change.
I think Naruto will address that with the Hyuga Clan after the war and Hinata will help with that so Neji will not have died in vain. I think that is a role Hinata will fill. I am not so sure that she will play a bigger role than any of the rest of K11 now, unless Kishi decides to let us know more about the byakugan since Kaguya has them too.
I do find it strange though that Hinata while falling under the genjutsu because she has rinnegan, she seems to be aware of what is happening to her where many of the others are not. Could it be that byakugan users while falling under the genjutsu do not go into the dream and are fully aware of what is happening to them?