While that is an interesting proposition, it wouldn't quite be the same. History repeating is a likely thing, but Alexander's situation is a bit different. The events surrounding Alexander are one big causal loop - they've already happened, so nothing we do can change a single thing in regards to the events surrounding Alexander.
On the other hand, the Ascians do seem to be putting effort into their actions. If the events surrounding Hydaelyn, Zodiark, and Rejoinings were a causal loop, they wouldn't need to bother (or at least not need to worry) - things would be guaranteed to play out in a certain sequence because they've already done so.
That's not to say a cycle similar to a merging and splitting of Light and Dark hasn't happened in the distant past or future, but it would be a case of Eternal Recurrence rather than a Causality Loop.
An easier way to explain it would be to use another game as an example.
FFXIV: Alexander's events are one big causal loop. Everything that we do, all the battles we fight, have already been won, because if that were not the case it would create a temporal paradox. Time moves in a circle in this case: Alexander is summoned, sends Mide and Dayan back to the past, and is summoned as a result. Everything has already happened; within the loop we're just actors on a stage, reciting a script that has been played out before, forever.
Dark Souls II: in the context of the story, Drangleic is implied to have been built on the ruins of countless kingdoms that rose and fell before it. This will continue to happen time and again no matter what ending you choose; in the original release you had to take the Throne of Want, and doing so simply makes you the lead of this "production" so to speak (you Link the Fire and burn until the Flame splutters and fades and another Undead comes to replace you, or you take your place as the Dark Lord until another Undead defeats you and one eventually Links the Fire). An additional ending in the updated version has you turn your back on the Throne of Want and deny either of the original endings, but even that makes no difference in the end: an Undead will eventually Link the Fire, causing another iteration of the cycle. While it's not on a cosmic scale, this is an example of eternal recurrence instead of a causal loop - this sequence of events plays out over and over again, but with different actors on a different stage. This cycle goes on until entropy has caught up with the world by the time of III.
TL;DR Alexander is caught in a loop, while a hypothetical merging and splitting of Light and Dark over the eons is just a cycle.