Maybe Percy feels worthless because he constantly compares himself to others. In the fanfiction world, there could be characters who seem to have more power or popularity, making Percy feel inferior.
In some fanfics, Naruto might feel unwanted because the author wants to explore a darker or more angsty side of his character. They may show him being excluded by the villagers even more than in the original story, perhaps to create a different kind of character development arc where he has to overcome not only external enemies but also this sense of being an outcast within his own community.
One reason might be related to his sense of responsibility. Naruto feels a huge obligation to protect the village and his friends. In fanfiction, when things go wrong or he fails in some small way, he could start to feel undeserving of all the good things in his life. He might think that if he can't fulfill his duties perfectly, he doesn't deserve the love, the power, or the status he has. Also, his own high standards for himself, which he has developed over the years of trying to prove himself, can make him feel unworthy when he falls short in any way.
Percy is very brave. He doesn't hesitate to jump into dangerous situations, and Annabeth knows that he'll protect her. So his courage makes her feel safe.
One reason could be its complex web of characters and plotlines. Fanfiction often features a large number of characters with their own stories intertwined, just like in Game of Thrones. There are so many different houses, characters, and sub - plots that it gives a sense of being a creation by a passionate fan rather than a more streamlined traditional narrative.