Just throwing some musing into the pot for consideration of what specifics we have and which are most likely to be at least partially true and relevant.
Minfilia's PowerPoint said that the corporeal form a primal is made of up aether from crystals and the land and such - when a primal dies, that aether goes back into the land to nourish it. If primal aether was lost or forever incompatible, the whole Realm Reborn scenario would have even more explaining to do because the damage caused by the Calamity was mitigated by Phoenix returning its aether to the land - Bahamut just interrupted the process and started eating the aether himself, causing neither the land nor Bahamut to be fully restored.
A primal's soul-like essence is what returns to the Lifestream, presumably to be blended back into aetherial atoms like the soul of whatever responded to the primal beacon to be rematerialized in the first place. Whether that is somehow tainted of incompatible with the Crystal in the sea... not sure, though it'd put a funny twist on the Primalsplosion in the 1.0 cutscene with the detonation of the seal, lol.