One reason could be that he feels misunderstood by the villagers. Despite all he has done for Konoha, some still hold grudges or are afraid of his power. Another might be that he wants to explore the world on his own terms, away from the responsibilities and restrictions of Konoha. Maybe he also feels a sense of loneliness there, as he has lost many important people and the village constantly reminds him of those losses.
His departure would definitely put a strain on his relationships. His close friends like Sasuke, if he is back in Konoha at that time, would have mixed feelings. They might worry about Naruto but also be a bit angry that he left without consulting them. Naruto's younger friends like Boruto would be confused and miss him a great deal, and this could lead to some distance in their relationships.
From a security perspective, Konoha would be weaker. Naruto is a very powerful ninja, and Hinata is no slouch either. Their skills and abilities would be missed. Enemies might see this as an opportunity to attack Konoha. Also, Naruto has been a symbol of hope for the village. His departure could lead to a decrease in morale among the villagers. They might start to feel less secure and more pessimistic about the future.
It would create a sense of panic. Naruto is a very important figure in Konoha. His strength has been crucial in protecting the village. Without him, the villagers would fear attacks from other villages or threats from the Akatsuki. For instance, if the Akatsuki knew Naruto had left Konoha, they would likely see it as an opportunity to capture him more easily.
Perhaps the fanfiction could focus on Naruto's adjustment to the new environment in Konoha. He'd have to get used to the different training facilities, local customs among the ninja clans, and the overall layout of the village. For example, he might struggle at first to find his way around the various training grounds and meet - up spots for ninja teams. But as he explores, he discovers hidden gems in the village and forms closer bonds with the villagers.
Another reason could be for the sake of protecting the village. Maybe he discovers some sort of threat that he believes he can only face by leaving Konoha. He doesn't want the village to be in danger because of him, so he runs away to draw the danger away from Konoha.
He adapts by using his natural resilience. Naruto has always been a fighter, so in fanfiction, he would quickly find ways to make the best of his situation. He might use his skills to get odd jobs at first to survive.
One possible reason could be that he felt misunderstood. In the village, Naruto was often ostracized despite his good intentions. Maybe he got tired of trying to prove himself and just ran away. For example, when the villagers still saw him as the nine - tailed fox rather than Naruto, it might have pushed him to leave.
Iruka sensei is almost certain to be in it. He has always been important in Naruto's life. Also, Sakura might be there. She could be one of the first to welcome Naruto or perhaps she might initially be a bit cold because of her past feelings for Sasuke. Other characters like Kakashi sensei could also make an appearance, guiding Naruto in his new life in Konoha.
In fanfiction, Naruto's life away from Konoha could be full of self - discovery. He might meet new and strange people who don't know about his past in Konoha. He could learn different fighting styles and develop his skills in unique ways, without the constraints of Konoha's rules and expectations.