I don't think it makes sense to attribute that specific power of breaking up Zodiark just to her elemental affinity though? Umbral and astral are depicted as polar opposites, and one has no distinct (known) advantage over the other. If we assume that Zodiark is stronger, and that he fought back at all, it wouldn't make sense that he lost in one "hit" (or at all).
If she was summoned to "keep Zodiark in check", then one would assume the summoners gave her specific powers that would make it possible, given the difference in strength. I guess keeping him in check technically includes slicing him and the world up, sealing him, but then that would imply that she was either designed to do so from the start, or that her creators miscalculated somewhere, did not expect this outcome, and Hydaelyn came up with a convenient solution by herself which ignores the difference in power.
Or, as mentioned, its possible that Zodiark just didn't resist at all. After all, for all we know Zodiark might've been just a mindless wish fulfillment device (which might also explain why the effects of his tempering seem to be as lax as they are). If such is the case then I fully agree with your train of thought.