It sort of works really well. Eiki is already a character who openly speaks her mind even if it causes people to dislike her (since she commonly will lecture others about their mistakes) so Satori's powers shouldn't bother her too much (or at all), the two of them are hated for basically the same reason, knowing too much about you to the point that they can easily use that info against you.
Outside of that, Satori sort of oversees the vengeful spirits from old hell, which are said to be stuck there permanently and are unable to reach heaven even if they are innocent, so she could work with Eiki to fairly judge those souls to move on instead of being stuck in a place of hell that is no longer managed by the Enma.