One reason could be that the writer has outgrown the Naruto fandom. As people grow and change, their interests shift. They might find other anime or stories more appealing now.
Sasuke could end up in a very dark place. He might get involved with some really bad characters or groups that could lead him further astray from his original path. He could lose his sense of self and become consumed by revenge or whatever negative emotions are driving him to leave in the first place.
One popular Naruto fanfiction could be about Sakura leaving Naruto due to feeling overshadowed by his power growth. In this type of story, she might decide to go on her own journey to find her true self and power, away from Naruto's shadow. This can lead to a series of adventures where she meets new characters and discovers new jutsus.
One reason could be that Naruto might feel he has outgrown Jiraiya's teachings in the fanfiction. He may want to explore his own path independently. Another possibility is that Naruto gets involved in a mission or a situation where he has to part ways with Jiraiya for the greater good. For example, if there is a threat in a far - off land that only Naruto can handle, and Jiraiya has other commitments elsewhere.
One reason could be to seek more power. In some fanfictions, Naruto might feel that the Leaf doesn't offer enough resources or training for him to reach his full potential. So he decides to leave to find a place where he can grow stronger.
One possible reason could be a difference in their goals. Naruto is from the Hidden Leaf Village with a mission to protect it and promote peace there. Rias, on the other hand, has her own responsibilities in the Underworld. Their conflicting duties might lead to Naruto leaving.
The relationships within the village would be severely affected. His friends would be heartbroken and split into groups, some trying to find him, others blaming themselves. The new generation of ninjas would also lack a role model. And the balance of power in the ninja world could shift, as other villages might see Konoha as weakened without Naruto and try to gain an upper hand.
One possible reason could be that Naruto feels he has learned all he can from Jiraiya at that point. Maybe he wants to explore his own path independently and test his skills without Jiraiya's constant guidance.
One reason could be to protect Konoha from a great danger that he can only face by leaving. Maybe there's a powerful enemy who has a vendetta against Naruto but would spare Konoha if he goes far away. Another reason might be a sense of self - exile due to some event that made him feel he no longer belongs in Konoha, like a misunderstanding where the villagers turn against him again.
One reason could be that Naruto discovers some dark secrets about the village that make him lose faith in it. Maybe something related to the 'dark sage' in the story reveals a side of the village's history or leadership that he can't accept. Another reason might be that he's framed for a crime he didn't commit, and instead of waiting for the village to believe in his innocence, he decides to leave. It could also be that he feels restricted by the village's rules and wants to explore a different way of being a ninja, which the dark sage figure represents in some way.