Maybe the writer is a big fan of both series and wants to create a unique and unexpected scenario. By having Rias abuse Naruto, it flips the script on the usual hero - villain dynamic. It also allows for a new exploration of character development for both Naruto and Rias, as they are put in very different circumstances than their original storylines.
One reason could be to explore a darker side of crossovers. Writers might want to see how a typically positive and powerful character like Naruto would react in a situation where he's being abused. It can create a lot of drama and tension in the story.
Well, it might be that Rias sees Naruto as a rival in terms of power or influence in a new setting. So, she uses her devilish powers to abuse Naruto. In the story, Naruto could start out confused and hurt but then draw on his ninja training and positive relationships back home to slowly turn the tables and make Rias see the error of her ways. Maybe he even teaches her about friendship and loyalty, which are concepts not as prominent in her world.
One reason could be to explore complex psychological and emotional states. By making Percy abused and mute, the writer can delve into how a character copes with trauma and isolation. However, this is a very dark approach.
There are several possible reasons. For starters, some writers might want to create a contrast to the original Naruto story. In the original, Naruto is mainly driven by the lack of recognition from the village. By adding this abuse element, they can show a different source of his pain and motivation. Also, it could be a way to experiment with different character developments. Maybe they think that Naruto could have had a more complex personality if he had to deal with abuse from his father. Additionally, it might be just for the shock value, to attract readers who are interested in darker and more complex storylines.
One reason could be for shock value. Writers might want to create a story that stands out from the typical Naruto fanfictions. By introducing such a dark and unexpected element like abuse, they can grab readers' attention. Another reason could be to explore a different side of Sakura's character. Maybe in this fanfiction, they want to show a corrupted or extremely stressed version of Sakura who takes out her frustrations on Naruto.
Some authors might write it to add a new and unexpected twist to the Percy Jackson story. They may want to see how the other characters would react if such a thing happened. Also, it could be an attempt to explore the psychological impact on Percy in a very different and extreme situation, though this is a rather controversial approach.
One possible fanfic idea could be that Sasuke discovers Naruto's abuse by the villagers early on. Sasuke, having his own dark past, feels a sense of kinship. He starts to protect Naruto in secret, which gradually evolves into a deeper bond between them. This could lead to them training together more intensely, not just to become stronger but also to find a sense of belonging in each other.
Perhaps there's a power struggle in the story world. Percy might be seen as a threat to certain groups or individuals who then resort to abuse as a means to gain control over him. Another reason could be related to his family background. If his family has some sort of enemies, they might take out their anger on Percy.
One reason could be to create a more complex character arc for Sakura. By giving her such a difficult past, it makes her growth and development in the fanfiction more interesting.
Maybe it's because of the different power systems. Naruto has chakra and his ninja abilities, and Rias has her devil powers. If in the fanfiction these power systems are not properly integrated or if one overshadows the other in an unappealing way, Naruto could be depicted as hating Rias. Say, if Rias' devil powers are made to seem too overpowering and it goes against Naruto's sense of fairness in combat, it could lead to such a scenario.
Another possible reason is that Naruto might be protective of his own story's integrity. He has been through a lot in his own series, and the Rias fanfiction might seem like an intrusion or a misappropriation of the idea of fictional characters. It's like his world and story are his own, and the fanfiction is trying to merge it with something else in a way that he doesn't like. He may feel that his own story should be kept separate from this other fan - created content.