I know remember during imaginary scramble Gilles talks how the Foreigner's that are the outer gods priestesses never needed to use the summoning system to be summoned, the outer gods just choose to use it cause it's convent and more fun that way. He says Gaia and Alaya literally could not stop them from doing what they wanted, but they love humans and they made it more convent for them to do it the right way, so they do.
I feel like it's kinda spooky how powerful they are, so they kidna hand wave them out of any real fights.