Perhaps he's seen the downsides of being a god in the Percy Jackson universe. Gods are often restricted by their domains and have a lot of responsibilities. Percy, who has always been a bit of a rebel, might not want to be tied down by such rules. He likes his freedom to make his own choices and help people in his own way, not in the way a god is expected to.
One possible reason could be that Percy values his humanity. He has seen the flaws of the gods and doesn't want to be like them. In the original series, he has had many experiences with the gods' self - centeredness. So in fanfiction, he might turn down godhood to stay true to his mortal self.
His decision might give hope to other demigods. They see that it's possible to be content without striving for godhood. For example, some demigods who might have been jealous or envious of Percy could now see that there are other paths to a fulfilling life.
One reason could be for a fresh take on the story. Writers might want to break away from the typical demigod narrative and explore a darker, more supernatural side of the Percy Jackson universe. Another reason could be to create a more complex and morally ambiguous character. By making him a demon, they can introduce new conflicts and relationships.
One possible reason could be power politics among the gods. Poseidon might see Percy as a liability in some complex power play. Maybe other gods are pressuring him to distance himself from Percy for some hidden agenda. Another reason could be a misunderstanding. Percy might have unknowingly done something that Poseidon misinterprets as a threat to his domain or power. For example, Percy's actions in the mortal world might have unintended consequences for the underwater realm.
One reason could be that he values his humanity. He has friends and a family among mortals, and he doesn't want to lose those connections. Becoming a god would likely put a strain on those relationships.
Well, in fanfiction, one reason could be the loss of his friends. Percy has been through so many battles, and if he loses someone close like Annabeth or Grover, it could send him into a deep depression. Another reason might be the burden of his prophecies. He's constantly expected to save the world, and that kind of pressure can wear a person down over time.
One possible plot could be Percy having to deal with new powers. He might struggle to control them at first, like accidentally causing thunderstorms when he's angry. Another plot could involve other characters' reactions. His friends might be in awe or a bit scared. For example, Annabeth could be worried about how this change will affect their relationship. Also, Percy could face new enemies who are jealous of his new god - like status or want to use his powers for their own evil plans.
In some fanfictions, Percy might be banished because he goes against the traditional ways of the demigod society too much. For example, if he tries to form an alliance with a group that the other demigods consider enemies. His actions could be seen as a threat to the stability of their world, so they banish him to keep the peace.
One possibility could be that Percy, as a new god, would have to deal with the complex politics of Olympus. He's always been an outsider, and now he'd be thrust into a world of power plays and ancient rivalries. Maybe he'd try to change some of the archaic rules that the gods have held onto for centuries.
One reason could be the overwhelming burden of his demigod duties. Constantly facing dangerous monsters and quests can take a toll on his mental state. He might feel like he can't escape this never - ending cycle of danger and responsibility.