There's also the issue with good king moogle mog. He was a benevolent person/non primal. But when he was summoned via similar methods as a primal he became corrupt and shares many traits of a primal.

My guess if that if one of the 12 was summoned the same way as the mog king (ascian method) then the same can happen.

They'll probably be the most powerful due to the fact that they are the patron deities of great nations.