Snow losing hope (heh eheh) doesn't bother me. He reacted pretty poorly to bad situations in XIII. It wasn't just when he learned the truth of Serah's focus, it was when Serah told him she was a l'cie, and when all those people dies when he was trying to rescue them. He doesn't know how to cope with the idea that heroism doesn't save, idealism isn't the truth, and bad things happening to good people.
But he reacted the same way to all three of those issues, which is where he sort of just blanked out and went quiet. This Snow is the governor of the City of Pleasure and dresses like a host. Granted existing forever in a time crash can change a man but wry.
Hope's transition is kind of awkward, there are some indications, he's continuously optimistic in the future and he takes initiative, but he's a genius who becomes the leader of the new world order ehhhhh that's a stretch.
There's a basis for Hope, Lightning, and Snow reacting like this but the narrative is still taking a few large leaps.