The issue I see is that if I'm not mistaken, FF XIV uses both approaches at the same time.
https://na.finalfantasyxiv.com/lodes.../#sidestory_08
Here in this side stories is established that those on the "bad timeline" didn't felt the effects of G'raha's actions and in fact realized they had created an alternative timeline. Then they decide to use what they had learned to better their own world. I quote:
"In my mind’s eye, I glimpsed a world where the Eighth Umbral Calamity had never come to pass, where Eorzea’s champion bestrode the realm, unbroken. But just as suddenly, I saw that this was G’raha Tia’s future, and not ours. Yet the skills we had honed to make that dream a reality were still ours to employ[...]And so our journey began anew. Would that G’raha Tia could see all that we will accomplish. Though we shall remain forever on different pages of history─and different books, besides─I take comfort in knowing we strive for a future of the selfsame brightness."
The time travel of EW is quite an issue precisely because it contradicts established lore of how time travel works while creating a paradox. Unless for some unfathomable reason Elidibus' magic works differently, what should had happened is that a third new timeline should had emerged where the events of that day would had changed the natural course of history.


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