I forgot to reply to this previously...
I'm really dubious about when or how that scene is supposed to fit. I feel like it may have been something they created early on as a "guiding concept" kind of thing but then the rest of the story shifted around it and they weren't willing to change it for whatever reason. I have to wonder if it's the only reason they stuck with the nonsensical "endless age of war" thing because they'd portrayed Ishgard in chaos there. (A better setup for the "dying world" idea seems to be the other implication that everything is simply falling into silence and the few survivors still might succumb to the aether-halting sickness of Black Rose. Everything in the world is inescapably fading and to "unwrite" it is simply to cut short those last hopeless moments with the promise that elsewhere things will be better.)
In any case, we're stuck with that. G'raha and Biggs are so desperately trying to research the historical records of the WoL's activities that they had to venture into wartorn Ishgard in search of Edmont's diarywhich is conveniently still in his intact study 200 years later. It lines up very well that G'raha is a historian and fully used to piecing together the past from various records. I assume they're gathering all the facts they can before deciding exactly when they need to set their target time.
I don't think Alexander "getting the cat to do the work behind the scenes" has any bearing on whether our actions there could damage the timeline or not.
We travelled to "three years ago" and - if you want to suppose that time travel inherently creates a different version of time to the original - created a "new" version of what happened to Mide where Backrix dropped his book for Quickthinx to pick up... which is a logical impossibility because Quickthinx already has that book before we travel to the past. Therefore there has to be one circular version of events - there can't be a version that happened without him possessing the book in the first place.
Yes, the cat is the reason that he acquires the book. But that's not the reason why we are already in the timeline where he has acquired the book, prior to travelling back in time to 'give' it to him. This is a plot absolutely relying on a single consistent time loop, therefore time travel cannot automatically split the timeline or the plot cannot work.
As for comparisons to other stories... I don't see any reason to assume there's some kind of "time-correcting monster" coming after us until it happens. It would seem very out of nowhere.
The suggestion or expectation was that at the point where the dark timeline is averted, G'raha and the tower's existence would simply unravel. Though of course it's entirely speculative as to what would actually happen, what such a thing would look like, and what remains vs what reverts to how it was. Raha goes, of course, and the tower because he brought it there... but what about the rest of the Crystarium? Does the city fall apart as parts of their building materials vanish into thin air? What about their memories of him being there?
It's simply a lot less messy from a writing standpoint to make his presence here permanent, whatever exactly you want to say happened to the timeline he came from. Still not impossible though.
Are you talking about the general area of the Twinning being in disarray? I assume everything got thrown around when it teleported... at least that's my best invented explanation for how the thing is full of uncaged Allagan beasts. Maybe they were all down there in their stasis pods while the Ironworks were (rather nervously) building the time machine, and warping across time and space leads some of them to not get put back exactly where they were... say, a few metres to the left, just outside of the pod. (And one S-rank chimera just outside the sealed main door, judging from the hunt mark description...)
If you're going to delete part of a post, you have to be careful about what you cut out, though. You need to leave the initial "(QUOTE=Name;12345)" bracket intact and only delete the stuff that comes after that. Otherwise the system doesn't recognise it as a quote and can't apply the correct formatting for it.
Beyond that, as long as the initial and ending (QUOTE)(/QUOTE) tags are left intact, you can easily delete what you want out of a quoted post, especially if you just want to respond to a particular part of it.