"Could have had"? That is what we have, except with the possibility that the old timeline split off rather than ceased to exist.
It does not imply that it "is a given that alternate timelines means infinite multiple timelines". I don't think there's evidence for that in this story at all.
As I wrote earlier, how it is described - and taken in combination with information from Alexander - implies that there is ONE split in the timeline created under extraordinary circumstances where a time traveler interfered with the past of their origin timepoint, making it impossible for events to lead back to their original time.
ie. If G'raha simply traveled back in time but didn't change anything, only watched it happen, he would witness the Eighth Calamity and eventually see his younger self released from the tower and prepare to travel back in time. There would only be one stable (but dying) timeline.
Instead he has prevented the Calamity that happened in his original timeline, making it impossible to see those same events play out. He has "changed tracks" and is now on a different path that will not lead to the timeline he originated from. This (I believe) is the one time that the timeline splits as a result of his actions, forcing both timelines to exist because they are both part of 'his story'. Once that single split has occurred, there won't be another one because there is no pre-established future for him to contradict from this point onwards.
The exact way he describes the plan to change time (in his conversation with Urianger) is a to create a "crossroads" - one deliberate point where we can take one path or the other.
Also interesting: the bit about the Namazu implying that - assuming we can trust Gyoshin's visions and Seigetsu's interpretation - he might be able to receive visions from the good future and not just the bad one, though perhaps only prior to "reaching the crossroads" and going down the other path.
From my take on it: no, you can't.
You can't just "visit another timeline" and do this for the satisfaction of knowing he survives somewhere - you would travel back in time to that point, rescue him right in front of your very confused younger self... and you've split the timeline, because that is definitely not how you personally saw the event play out last time.
So now you're on a different path of history to the one you arrived from - can you return to the "present"? Or would you travel forward in time to realise you're still in that altered timeline where the other version of you - the one that saw you rescue Haurchefant - is the Warrior of Light doing all the Warrior-of-Lighty things you did. Meanwhile, you're stuck (and your 'home timeline' is minus a WoL) until the Ironworks manage to go an extra step in figuring out how to cross not only time and dimensions but also timelines. So good luck with that.



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