Revelations from Patch 3.5

[Alberel]

I'd argue that we have.

Wasn't Phoenix summoned under similarly extreme circumstances?

Come to think of it:

Yes, you're right. Whilst the original summoning of the Twelve to restore Dalamud was performed using the collective faith of the entirety of Eorzea, the creation of Phoenix was born of their desperation when the Twelve failed them. The situation at Baelsar's Wall is very similar.

Come to think of it, is it not then possible that Ilberd may actually have created a new primal as Louisoix did? In both cases the faith component of the summoning ritual was replaced with undirected desperation. The summoning was not focused on a specific deity. I wonder now if Ilberd is truly dead... He may have actually become a primal.