As everyone already mentioned, he considers it more Emily's world than anything else. Let's be honest, he barely knew anything about magic four months ago. Having him ruling a declining magical kingdom in time of war seem a recipe for disaster. At best, most people would probably be terrified of his presence in the meeting room to make anything productive. To remind you, he's a god with history of setting castles with people and workers in it on fire. At worst, some ignorant staff or noble would infuriate him to set them on fire every time. Again, not really productive. Best to stick to what he's good at: slice and dice, fireballs, reality bending, and the occasional soul crushing. Those, and gathering followers and tools for the fight.
Though it's not to say he can't learn to do it. And he did bring out ideas that are excellent, though Emily did the minutia of implementing them. So it might happen over the course of years or decades without Sorcery. Which is fine IMO. The cast's lifespans are in the thousands of years, at least by beginning of B2. And in B3, he and the Chosen are practically ageless because of Faith.
As for the throne, I'd imagine he's the one sitting on it during the times he's meeting people during the War Council portions of the game. Though without the renders for it. He did say his barstool upgraded to throne. I could be wrong on this though.