Maybe the writer wants to make a statement about the darker side of a fictional world. They could be using Percy's situation to show the potential for evil or neglect within the story's setting. But it's also a very controversial way to do so. Another possibility is that they are trying to create a very different, edgy version of Percy's character, but this should be done with care as it involves sensitive topics.
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.
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.
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.
There might be some very niche fanfics out there with this concept, but I would be cautious. Abuse and muteness are serious topics. A lot of fanfic communities tend to promote more positive and less disturbing content. So, it's not easy to just recommend one off - hand.
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.
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 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.
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.
One reason could be to explore the darker side of Percy's life. His story is mainly about his heroics, but this could show what he endures at home. It also might be to create more depth to his character by showing how he copes with such a difficult situation.
One possible reason could be a misunderstanding. Maybe Percy does something that Annabeth misinterprets, leading to a rift between them. For example, Percy might make a decision during a battle that Annabeth thinks is too risky and endangering others, and this causes a big argument that results in their separation.
One possible reason could be a misunderstanding. Maybe Artemis misinterprets Percy's actions as a threat to her or her hunters. For example, if Percy accidentally endangers one of the hunters while trying to save someone else, Artemis might see it as a betrayal of her trust in him to respect her followers.