One possible reason could be feeling betrayed by the village leaders. Maybe they made decisions that Naruto strongly disagreed with, like how they treated certain groups or individuals. If Naruto felt that Konoha was no longer the place that stood for justice and fairness as he once believed, he might abandon it.
One possible reason could be fear. Naruto has the Nine - Tails within him, and some in Konoha might be too afraid of its power getting out of control. They may not fully trust Naruto to keep it in check.
At first, Naruto is likely to be heartbroken. Konoha has been his home, and he has always longed for acceptance from the villagers. So being abandoned would be a huge blow to him.
One possible reason could be that Naruto discovers some dark secrets about the village leadership that go against his values. For example, if he finds out that they have been using underhanded means to maintain power.
This fanfiction might make Naruto more of a loner. In the original, he was always surrounded by friends and the support of the village. Abandoning Konoha would force him to rely only on himself and his own powers. His character could become more cynical as he distances himself from the place he once called home.
One reason could be that Naruto has seen too much death and destruction in Konoha. His 'godlike' state might make him think that the only way to end all the suffering is to destroy the root cause, which is Konoha. He may believe that Konoha's system is so broken that it can't be fixed and needs to be completely eradicated.
Another reason might be that Naruto is seeking a greater purpose. In the fanfiction, his 'godlike' state could make him realize that there are threats out there that he can't face while being tied to Konoha. He may leave to protect the world on a larger scale, believing that he can be more effective away from the village.
One aspect of 'dark godlike Naruto Konoha bashing fanfiction' could be the exploration of Naruto's character in a much darker and more powerful way than in the original series. In these fanfictions, Naruto might turn against Konoha due to some past grievances. For example, if the village had treated him even worse than in the canon, he could develop a vengeful side. Maybe he discovers some dark secrets about Konoha's leadership and decides to take matters into his own hands, using his new 'godlike' powers to challenge the status quo.
As for Kakashi, he would be in a difficult position. He has mentored Naruto and also has a strong loyalty to Konoha. He might try to understand Naruto's reasons while also having to deal with the village's reaction. Their relationship could become strained as Kakashi tries to balance his duties to the village and his connection with Naruto.
Many relationships would be affected. For example, Sasuke's story would take a different turn. He might not have the same motivation to return to Konoha if Naruto is not there. Also, Naruto's other friends like Sakura would be devastated and might set out on a journey to find him. The power dynamics in the ninja world would shift as well, with other villages possibly seeing Konoha as weaker without Naruto.