I wouldn't say that the idea of alternate timelines as part of canon or tampering with time was necessarily implied by the Omen trailer. It was listed as an alternate universe in a presentation designed to show how the parts of the XV Universe fit together, true, but BD2 also made it clear that the CG house that developed the trailer were allowed to come up with their own interpretation of XV's concepts without being given exact instructions on what to show. As far as I can tell, the events in the Omen trailer (except, perhaps, for the dialogue) and the events in the game are entirely distinct rather than interdependent the way they would be had they been designed as canonical alternatives to each other.
With that said, Ardyn definitely has some degree of time powers given what happened in Chapter 10, so extending them from the ability to stop time and mask his appearance to the ability to undo a recent choice that resulted in massive failure wouldn't be that crazy. Likewise, it wouldn't be entirely unreasonable for Bahamut, as the source of the Lucis Caelum powers, to be able to do that, either.
All that really needs to be done to avoid the issues KH ran into with time travel is to combine simple rules with very limited use cases. Perhaps reversing time results in the timeline being literally written over and no one has the power to do so for periods longer than a day. If said power is given to Bahamut rather than Ardyn, it wouldn't even necessarily raise the question of why the power was never used during the main game, since Bahamut wouldn't really have any reason to undo anything. (Of course, if that's the path that was chosen, I would expect the Dawn of the Future path to involve Noct fighting Bahamut, taking that power for himself, and rewriting two thousand years worth of history to bring about the ultimate happy ending for everyone. =P )