I propose again to you the Time Travel Tragedy. We have seen 4 anime discussed with regards to their adherence to tragic convention. And although there are other genres at work within the narratives—mystery, romance, science fiction—it is ultimately the paradigm of the time travel tragedy that sets up the story and guides the character arcs. We have four tragic heroes, the inevitability of a god-driven fate, and parallel tragic events.
And in conjunction with detective work to solve the mystery of how each world’s “gods” and tragic events function—as well as the opportunity to overcome one’s tragic flaw—we see a light at the end of the tunnel: possibly a happy ending. This is a modern tragedy. And time travel is the vehicle by which such stories and mysteries are created.
[ sources: wikipedia and wikia (for reference), Poetics (Aristotle), the anime themselves]