Is 'Hydaelyn' a misnomer based on a misconception?

[Lersayil]

Except that isn't Hydaelyn's purpose at all, according to Hythlodaeus' shade. His account of it (which is probably the closest thing we have to an unbiased account) is that she was created because some of the Ancients felt "enough had been sacrificed to Zodiark - that [the post-Terminus] world should belong to the new lives newly born" instead of those selfsame new lives being sacrificed to Zodiark to bring back those Ancients who sacrificed themselves to create and empower him. Simply put, she is the embodiment of the idea that the future should belong to those living in the here and now, not ghosts of the past. Her actions are bent toward that idea, but due to the power disparity between the two (Hydaelyn has, at most, 1/8 of Zodiark's full power) she had to sunder him to fulfill that directive. Unfortunately due to his status as "the will of the Star," that sundered the planet in the process; the rest is history. (Actually destroying Zodiark through force would likely have even more disastrous consequences.)

There is a void of information on that matter. We kinda know why she was summoned. But I don't think we have any idea what her concrete purpose and directive was (is) that the creators bestowed on her? I doubt she was just manifested as an ideal. Defeating something much stronger would imply some premeditation.

We're told creation magic worked by having a pretty good image of what you were creating. Unexpected things happened, but I think its unlikely that she came to be with dimension slicing powers by accident.

It's probably safe to assume that defeating Zodiark was always part of the plan. Not sure about the rest though. She sorta took up guard duty afterwards, trying to embody the ideals you mentioned? It might be her own will, nature, a design feature, or all of them. Either way an imperfect system, seeing how more than half the shards are gone.