Well, based on the Mothercrystal's dialogue early in the storyline, and the events in the ending, it's apparent the Crystals of Light are
effectively manifestations of Hydaelyn's 'will', hence the name - with the Ascians using Dark Crystals to further their plan to rebirth Zodiark, it forces Hydaelyn to employ the same methods with her agents, ala, the player. Although it wasn't obvious upon gathering all of them, their true purpose only became known when facing Lahabrea - the six crystals formed 'the Blade of Light' eluded to by Louisoix in his journal, which the player used to free Thancred from Lahabrea's control (and thus making that lauded synthetic 'dark crystal' Minfilia ordered from the Students of Baldesion nothing but a red herring). Hydaelyn knew a show down with the Ascians was inevitable, and thus had to ensure her champion had the tools to do that - the Echo itself wasn't enough. Those tools are the Crystals of Light.
Or at least, that's what it seems to me.

Originally Posted by
Yasminou
Hi,
If I recall correctly, we do receive all 6 elemntal crystals during the story, even though 3 Primals remain. I think for instance we receive the ice crystal at the end of Stone Vigil. However, I don't remember how we received water and thunder crystals. Maybe we will know more in 2.2 quests with Leviathan...
We in fact do - four are in fact gained from the Primals (three after defeating Ifrit, Titan and Garuda, the fourth is Ramuh's one that was handed over by the sylphs), with the remaining two left over from pseudo-summonings of random monsters by the Ascians (ala, the dragon at the end of Stone Vigil and the very first one after defeating the golem early in the story). Another crystal is briefly seen on the ground after defeating the 'masked mage' and his gargoyle pet during the starting nation's storyline, although it soon disintegrates. But the elements are definitely represented by the Crystals of Light, even if not all of them are gained from Primals. It's obvious that a Crystal of Light just requires significant aether concentration, and is not necessarily just from a Primal.