I don't know if anyone has mentioned it yet, but...
When discussing the pixies' childlike temperaments, Alphinaud (I believe) conjectures that souls may not dissolve in the Lifestream, but still exist as independent packets. This is why pixies are the reincarnated souls of children - their existence persists in the Lifestream until they are reborn. Handily enough, this also explains doppelgangers on the First - Gerolt's doppelganger just has another piece of his otherwise fragmented soul, which is why they are for all intents and purposes the exact same person. (His First counterpart just has long flowing hair instead of being bald.)
It's not like this is a new concept for Final Fantasy, either - it's possible to persist in the Lifestream of VII with a strong emotion, though this tends to degrade the personality of those who do so. President Shinra and Septhiroth both manage it through greed and hatred, respectively.
The events in Amaurot suggest the Warrior of Light / Darkness is the reincarnated soul of an ancient Ascian - Emet-Selch's good friend Hythlodaeus no less - and that their overwhelming strength is owed to them having the soul fragments of their other selves that were rejoined through the Ascians' machinations. Ardbert was their First counterpart, who seems to willingly merge with the Warrior of [Light / Darkness] to help stave off the corruption from the Lightwardens' power until it's used to finish off Hades.