The way I saw it, the Ivalician summons (Mateus, Shemhazai, Adrammalech, etc) are the "primals" of the Ascians... dark versions of the Twelve gods that most of Eorzea worships, with their primary god being Zodiark, the 13th Zodiac. Opposed to Zodiark's darkness is Hydaelyn, the spirit of the planet, and Her Light. Further evidence supporting this is the names of all the Ascians revealed so far being associated with the Ivalician espers... For example, Lahabrea is associated with Mateus, so we could see Lahabrea summoning Mateus in the future...

Eventually it'd be cool to fight all those dark primals. But since there's so many it might be unreasonable to assume we'd get them all...

As for the primal/elder primal debate, as far as I know, the only Elder Primals confirmed so far are Bahamut and Odin, correct? Midgardsormr as a Primal could be cool - I like the theory that the Dravanians' faith revived him as a primal.

Nidhogg the Wyrmking COULD be a Primal. We don't know yet.

I'd love to see Alexander as a Primal in Ishgard, but since he's mechanical in every version of him so far it might be a little far-fetched... I think it's more likely that he'd be another Allagan weapon, perhaps one secretly built to counter Ultima Weapon?

Knights of the Round could be interesting!

But they also said we'd get totally new Primals unseen in any FF game before, so bets are off as to what those could be.