Is summoning just advanced arcanima though?
Magic can't create anything truly alive, even the Ancients never figured out that trick, and the actual primals seem pretty alive to me. You telling me that the glee Susano felt as he battled us was fake? I'm not buying that
I think the summoning that the Ascians go around teaching is more akin to necromancy than creation magic, or even arcanima. I reckon that when the Amalj'aa summon Ifrit, they keep pulling the same poor long dead soul out of the lifestream and chucking him into a new body they make for him. In theory they could just use all those crystals to create a giant glorified egi, but without the soul to make it truly alive, it'd still be more akin to a pet than a deity.
Plus, teaching a broken form of arcanima that messes with circle of life seems like exactly the sort of asshole behaviour that the Ascians would engage in.