SC pretty much stated it when Parallax was forced back into the Earth GLs lanterns that Earth GLs were the best at overcoming their fears, hence being suited to carry Parallax in their lanterns.
None of them carry the entire Parallax, right? They all have small part of it. When he comes out and takes on a host(even GL host), they have little chance of stopping him.
Dude was omniscient. Killed and resurrected himself. Went to Those Who Sit Above In Shadow and flat out demanded they cut their shit. Went to Surtur's realm and treated him like some low-class peasant. RKT showed zero fear in that arc. Even realized he had to let Sif die, and was okay with it.
All knowing=/=fearless.
Besides, Parallax will put the fear in him.