Kaptain Kuba discusses the lore of GOW from the first game through the entire series, following the well worn theory of Kratos actually being the God of Death and how it informs his decisions in many cases. Decisions that would otherwise not make much sense.
The idea of some type of 'mutiny law'...where if a god is killed, the killer inherits their position is interesting. It also means though that Kratos would inherit most of the gods roles in the Greek pantheon. Not just the God of Death (Thanatos).
If you have time, check out the video and share with us your preferred theory on Kratos!