How does a Chunin put up a fight against an opponent that's on a tier above Kage? Hinata is like a regular civilian to him. This was an opponent who blew up the whole village with 1 jutsu. She only even got to speak in the manga because he wanted Naruto to be emotionally devastated.
Hinata was used as a plot foil in the Pain arc, and Neji was used as the plot foil in the end.
If Hinata died in the Pain arc, nothing in Naruto's story would have changed. But because Neji died, they use that as the excuse for pushing Hinata into Naruto. But really it's the same — Neji's death should have no impact whatsoever on the future trajectory of Naruto's life. Both art plot foils.
Imagine if Sakura died. Or Sai. Or Kakashi. Or Iruka. Just like Jiraiya, these people had a meaningful positive impact on Naruto's life. The flashbacks are of memories where those people interacted with Naruto.
However, for Hinata, there are no flashbacks with Naruto because they literally never interacted. And for Neji, the only flashbacks are from the chunin exam where Naruto went after him for being a jerk. Sure, Naruto won and changed Neji's mind, but being an obstacle in a fight is a far cry from having some kind of teammate bond.
Early in the manga, Neji is shown as being aloof and supremely skilled. More on Sasuke's level. Neji was shown to be fierce, aloof, and complex in his hatred of his clan yet loyalty to it — but by the end, he was homogenized to a squeaky-clean version of himself, a formerly fierce shinobi who was 'happy' to die for Naruto, the ninja who was now so far above every other flipping ninja alive.
Neji's death was a waste. If he'd been kept in his part one character, then he should have been caught off guard and disappointed in himself. Not dying the way Hinata tried to kill herself in the Pain arc — by defending a nin who didn't need to be defended.