Maybe he feels a sense of guilt. For example, if something bad happened in the village that he blames himself for, even if it wasn't really his fault. He could exile himself as a form of self - punishment. He has always been very hard on himself when it comes to the well - being of the village and his friends.
Another reason could be related to his search for power or knowledge. He might believe that he can't achieve what he wants in the village environment. So, he exiles himself to go on a solitary journey to find new techniques or gain a deeper understanding of his powers, away from the distractions and limitations of the village.
One possible reason could be the burden of his past. Naruto has faced a lot of hardships and the memories might be overwhelming him, making him want to be alone. For example, the loss of his master Jiraiya might have left a deep scar, and he might feel that isolating himself is the only way to deal with that pain.
It could also be due to a sense of guilt. If something bad happened that he blames himself for, like someone getting hurt because of him, he might exile himself as a form of self - punishment. He'd rather be alone and deal with his own pain than face those he feels he's let down.
Maybe he feels guilty. Suppose he made a big mistake, like accidentally leading an enemy to a safe haven of demigods. The guilt could be so overwhelming that he exiles himself to punish himself and keep others safe from his potential future blunders.
There are several reasons. He might be afraid of getting too close to people because he's lost someone important and is scared of more loss. It could also be that he's discovered some new power within himself that he doesn't understand and is worried about hurting others if he gets too involved. Additionally, there could be some political intrigue in the village. Maybe there are some people who are plotting against him and he's keeping to himself to avoid being a target or putting others in danger.
It could be a miscommunication. Maybe Hinata said something that Naruto completely misinterpreted in a very negative way, like she didn't love him anymore or she blamed him for something major. This misunderstanding could be so great that Naruto loses hope and takes his life.
One common reason is the feeling of inadequacy. Naruto often aims high and wants to be the best, so if he falls short in a fanfic's story, he may start to hate himself. For example, if he fails to master a new jutsu quickly enough or loses a fight he was expected to win.
Often, he first has to face the challenges of survival alone. He may encounter various new enemies in the outside world. For instance, he could run into rogue ninjas who see him as an easy target because he is alone.
One possible reason could be a misunderstanding. Maybe Naruto overheard something his family said that he misinterpreted as them not loving or believing in him. For example, if he heard them talking about his wild nature or his past mistakes in a way that he took the wrong way.
One possible reason could be extreme guilt. Maybe he fails to protect his friends in a major battle and feels so responsible that he can't bear it. For example, if Sasuke were to die because Naruto couldn't reach him in time, Naruto might sink into such deep guilt that he sees no way out but death.
Yes, such fanfictions exist. In these fictional scenarios, Naruto might kill himself because of Sasuke for several reasons. Naruto's whole life has been centered around Sasuke to some extent. If he feels that he has failed in his mission to bring Sasuke back to the right path and that the situation has become so dire that the only way to atone for his 'failure' is through his death, he might do it. Also, if Sasuke were to cause harm to someone Naruto holds dear, like the village or his other friends, and Naruto feels powerless to stop him in any other way, he could choose to end his own life as a last resort.