It could lead to political unrest in Konoha. There might be those who blame the village leadership for Naruto's departure. This could lead to power struggles as different factions try to take control and change the way the village is run. Some might demand more transparency and better treatment of their shinobi to prevent such a thing from happening again.
He could leave because of a broken heart over a lost love. If Naruto had strong feelings for someone in Konoha, like Sakura, and she chose someone else or rejected him in a cruel way, it might be too much for him to bear. So he decides to leave the place full of memories related to that person.
Konoha would initially be in shock. Naruto is a hero to many in the village, and his sudden departure with Itachi, who was once considered a traitor, would cause a lot of unrest. The villagers might start to question the leadership of the village, wondering why Naruto left and if there was something they could have done to prevent it.
Another reason could be that he witnesses corruption or unfairness within the village leadership. If he sees that the system is rigged against certain groups, including himself or his friends, he could grow to hate Konoha and decide to leave.
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.
This type of fanfiction concept is really out of the ordinary. Naruto's character is built on his values of friendship, loyalty, and his dream of becoming Hokage. Killing Sasuke would mean betraying all of that. However, in a fanfiction, the author might be exploring the 'what - if' scenario. For example, what if Sasuke's actions against Konoha were so heinous that Naruto felt he had no choice? But still, it's a far - fetched and very different view from the original Naruto we know.
If Sakura were to give Naruto a token made of sakura leaves as a symbol of their friendship, and then later break off all contact with him and leave the village, Naruto would be heartbroken every time he saw a sakura leaf. The once - positive association would become a painful reminder.
One possible fanfiction could be that Sakura, in a moment of great sacrifice, uses her chakra to turn into sakura leaves that Naruto has always associated with her beauty and kindness. But this transformation is a final goodbye as she is sacrificing herself to save the village. Naruto is heartbroken as he watches the sakura leaves scatter, feeling like he has lost a part of himself.
Konoha's power structure could be affected. Naruto is one of the strongest shinobi in the village. Without him, the village might be more vulnerable to attacks from other villages or threats. They would need to quickly find ways to fill the gap in their defenses.
Sasuke might be more understanding. Given his own experiences of leaving Konoha, he could respect Naruto's decision. However, he might also secretly plan to keep an eye on Naruto from afar to make sure he is safe.