This is crack...sorta. I don't know where else to post it.
You are aware of how Karura and Ucchushma were able to link to the priests and grant them spells, correct? It is my assumption that the demons can't do the barrier spells and the Fire Life Samhadi on their own.
They need a human to recite those spells (and reshape their power.)
What if all demons are like this?
What if SATAN is no different? Except if he were to partner with a human to recite for him, they would die. Rin is the only exception. He is half human, so he can still be the reciter for Satan and not die from it.
Furthermore, if Satan's blue flames are trans-dimensional like I believe (Blue Night, Rin destroying Mephisto's cage, the fact that Satan can ALSO cross dimensions with the Gehenna Gate), Satan can use Rin while he is still in Gehenna.
That's also why he agreed to let Rin go to cram school.