The power structure would be completely disrupted. There would be no more divine interference in mortal affairs, which could lead to chaos at first as there are no gods to control natural elements like the sea or the sky. But it could also lead to new opportunities for mortals to take control of their own destinies.
Perhaps in the 'Percy Kills the Gods' fanfic, there is a new and extremely powerful enemy that the gods are unable or unwilling to fight effectively. Percy sees this as a sign of their incompetence or callousness. He could gain some new, super - powerful abilities or weapons that give him the confidence to challenge the gods. He might start by targeting the more tyrannical gods first, like Zeus, who has a history of being harsh and unfair.
Gorr had a tough life. He was from a desolate planet. His people suffered greatly. He lost his family due to hardships and lack of resources. This led him to turn against the gods he once worshipped as he blamed them for his misfortunes.