Perhaps in a fanfiction, Sasuke discovers a new and extremely dangerous power that he can't control and it starts to endanger Konoha. Naruto tries to stop him but in the heat of the battle, accidentally kills him. Overwhelmed with guilt and feeling that the village will never understand, Naruto leaves. But this is a very different take on their relationship and the Naruto world as a whole.
Maybe they leave because of a conflict within Konoha. There could be political unrest or a group within the village that they don't agree with. They might think that leaving is the only way to avoid getting involved in something they don't believe in or to protect the village from the inside out in their own way.
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.
They might leave because of a prophecy. If there was a prophecy that Naruto would bring destruction to Konoha or that Konoha would bring destruction to Naruto, Kushina might take Naruto away to prevent it.
Economically, there could be some impact as well. Naruto and Hinata are popular figures, and their presence in Konoha likely contributed to the local economy in some ways, such as through tourism (people coming to see the famous Naruto). Their departure might cause a dip in certain sectors that relied on their popularity, but it could also open up opportunities for new shinobi to rise and bring in new sources of income for the village.
They may leave to investigate a mystery that has long been ignored or covered up by Konoha. This could be related to the origin of certain powerful jutsu or the real history of some important clans. Their departure from Konoha is a way to break free from the village - imposed limitations on knowledge and seek the truth on their own.
Maybe there are some dark secrets within Konoha that he discovers in the fanfic. These secrets could be related to the treatment of certain individuals or something more sinister about the village's leadership. Discovering such things could make Naruto decide to leave in order to distance himself from the corruption or unfairness.
One reason could be to seek a new life away from the constraints of Konoha. Maybe they feel that they can't fully grow or explore their potential within the village. Another reason might be to protect Konoha in their own way. They could believe that leaving and dealing with threats from the outside would keep the village safer.
One reason could be that he feels a sense of disillusionment. After the war, he might see that the village he fought so hard for still has deep - seated problems and prejudices. He might think that leaving is the only way to find true peace for himself. Another reason could be to protect the village from any potential threats that might target him. If he's away, those threats might not come to Konoha.
One reason could be to seek a new life away from the political drama in Konoha. Naruto has always been in the spotlight and has faced many political challenges. Hinata, being by his side, might support his decision to leave for a quieter place. Maybe they want to raise their family in a more peaceful environment, away from the constant threat of enemies targeting Konoha.