I would say that any God of War set in Egypt would need to go in a very different direction than the original Greek trilogy or the new Norse games. Mainly because the Egyptian gods weren’t all complete asses and have several tales where they are taking active part in protecting the world and the people therein. Kratos could end up facing down the armies of Set and Apep, sure, but then he wouldn’t have anywhere else to go in the story.
I also think it makes sense for the Egyptian God of War to be a local god because the last time a foreign god came around, their Egyptian asses were thoroughly kicked.
And I agree. Like Mimir said: "It's complicated."