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.
Well, it could be due to the failure to protect the village. Naruto has always been about protecting Konoha. If something really bad happened, like a major attack that he couldn't prevent and many lives were lost, he might feel so much guilt and heartbreak that he decides to leave. He would feel like he failed his purpose.
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.
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.
The village would likely be in chaos. Naruto has been a key figure in protecting the Hidden Leaf. Without him, there would be a power vacuum, and enemies might see it as an opportunity to attack. The villagers who once relied on Naruto would be filled with fear and uncertainty.
Maybe Naruto discovers that the village he has been trying so hard to protect has been using him all along. He might find out some dark secrets about the Hidden Leaf, like they were involved in something immoral and were just using his power, which would shatter his idealistic view of the village and leave him heartbroken.
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.
A theme that often pops up is the idea of growth. Heartbreak can be a catalyst for Natsu to grow as a character. He might become more empathetic or learn to be more cautious in relationships. Also, the theme of forgiveness can be present. He may have to forgive the person who caused his heartbreak to move on.
Naruto could also be deeply hurt and go into a state of self - reflection. He might question his own judgment in relationships. For example, he could think about what he did wrong or if there were signs he missed. This could cause him to leave to find himself and grow stronger on his own. He may start to focus more on his ninja training and his friends in the village, trying to move on from the pain of being cheated on.