It could be Sasuke. If he were to turn to the dark side in the fanfiction, his Rinnegan powers could be used to destroy Konoha. He has the potential to be extremely powerful and if he has some sort of vendetta or is influenced by some dark force, he might take his anger out on the village.
Well, it could be that the wielder of the Rinnegan has the ability to control powerful forces like the Six Paths techniques. They might use the Deva Path to create massive gravitational pulls that start to crumble the buildings in Konoha. Or perhaps with the Preta Path, they could drain the chakra from all the ninja in Konoha, leaving them defenseless against further attacks, which eventually leads to the destruction of the village.
One possible reason could be a search for power. The character might feel that Konoha doesn't offer enough resources or training opportunities for them to fully explore the potential of the Rinnegan. They may believe that there are other places in the Naruto world where they can gain more knowledge and power related to their special eye.
Another scenario is that Naruto leaves because he feels like an outcast with the Rinnegan. The villagers might fear his new power, and he decides to leave to find a place where he can fully understand and control the Rinnegan without causing panic. He could then encounter other powerful ninjas or groups who either want to use him for his power or help him master it.
Madara Uchiha could also be the main character in this type of fanfiction. Although in the original story his actions are mostly related to his grand plans for the Ninja world, in a fanfiction, it could be explored what would happen if he decided to leave Konoha specifically because of his Rinnegan and the power it holds.
His journey could lead him to the outskirts of the ninja world, to places that are unknown and full of mystery. With the Rinnegan, he might be able to access hidden paths or dimensions. He could be exploring these uncharted areas to gain more power and understanding, away from the politics and rules of Konoha.
The story could develop with Konoha facing various threats without Naruto's help. They might initially struggle and have to rely on their remaining ninja forces. This could lead to the development of new characters or the growth of existing ones as they are forced to step up. Meanwhile, Naruto could be off on his own journey, perhaps exploring the true nature of the Rinnegan's power or trying to create a new world order without Konoha's influence.
Perhaps Naruto with the Rinnegan has seen a darker side of Konoha that he was previously unaware of. It could be something related to the village's past secrets, such as hidden experiments or unjust actions towards other ninja clans. This new knowledge makes him so disillusioned that he refuses to offer his help. Also, he might have formed new alliances outside of Konoha that he values more and that conflict with Konoha's interests.
Their relationship would likely become more complex. With the Rinnegan involved, they might have to rely on each other more for understanding its powers. They could become more protective of each other, knowing the power and the danger it brings.
One implication is that he becomes much more powerful. The Rinnegan gives him access to powerful abilities like the Six Paths techniques, which would change the power dynamics in battles in the fanfiction. He could now face stronger enemies more easily.