It could also be that Naruto leaves Konoha in search of a greater power or knowledge. He might have heard of some ancient jutsu or a powerful sage that can teach him things that he can't learn in Konoha, and so he embarks on a journey away from the village.
In this kind of fanfic, one possible scenario could be that Naruto leaves Konoha due to feeling misunderstood. Maybe he has been wrongly accused of something and decides that he can't stay in a place where people don't trust him.
Maybe there are some dark secrets within Konoha that he discovers in the fanfic. These secrets could be related to the treatment of certain individuals or something more sinister about the village's leadership. Discovering such things could make Naruto decide to leave in order to distance himself from the corruption or unfairness.
One possible storyline could be that Naruto, feeling constantly neglected, decides to leave Konoha in search of a place where he can be truly accepted. He might stumble upon a hidden village that has its own unique ninja culture and there he begins to train in new and different ways, far from the scorn he faced in Konoha.
One possible reason could be for Naruto's safety. Maybe she has to go on a dangerous mission and believes Konoha is the safest place for him. Another reason might be that she is forced by some powerful enemies who threaten Naruto's life if she doesn't leave him in Konoha.
One possible consequence could be a shift in the power dynamics within the village. With Naruto leaving, there might be a lack of his unique skills and leadership, which could lead to new challenges for Konoha in terms of defense against enemies. Another consequence could be the emotional impact on his friends and allies. They would likely feel betrayed or worried about his departure, and this could strain relationships. Also, Naruto's leaving might expose some hidden secrets or issues within Konoha's heritage that were previously overlooked, causing a stir within the village.
One possible reason could be to seek stronger opponents outside of Konoha. Naruto might feel that he has outgrown the training opportunities in the village and wants to face greater challenges.
In such a fanfiction, one possible scenario could be that Naruto is experimented on for his unique chakra. Maybe Konoha scientists, in a bid to understand the power of the Nine - Tails within him, conduct various tests that are both physically and mentally taxing for Naruto.
One possible scenario could be that Naruto leaves due to a misunderstanding with Sasuke. Maybe Sasuke says something harsh about Naruto's skills and Naruto, in his pride, decides to leave. Another could be that Naruto feels he's holding the team back in some way and leaves to train on his own in order to become stronger without being a burden. Or perhaps there's a mission gone wrong where Naruto is blamed for something he didn't do, and he leaves out of a sense of unfairness.
One possibility is that Naruto realizes Sakura has feelings for Sasuke that he can't change, so he decides to focus on his own ninja journey alone and leaves her to figure out her relationship with Sasuke. He might feel that his presence is only causing confusion or getting in the way of her true feelings.
In such a fanfiction, one possible scenario could be that Naruto sacrifices himself to save Konoha from an ultimate evil. Maybe a powerful enemy like Kaguya returns in a more menacing form and Naruto, seeing no other way, uses all his power and gives his life to seal the threat away.
One possible plotline could be Naruto leaving Konoha due to feeling out of place because of the harem situation. Maybe he's overwhelmed by the attention of multiple characters interested in him romantically and decides to seek solitude or a new path outside the village.