It could be that Naruto discovers some secrets within his family that make him feel uncomfortable or out of place. For example, if there are hidden agendas or dark pasts that he doesn't want to be associated with, he might choose to move away to start anew.
One reason could be that he feels misunderstood by the villagers. Despite all he has done for Konoha, some still hold grudges or are afraid of his power. Another might be that he wants to explore the world on his own terms, away from the responsibilities and restrictions of Konoha. Maybe he also feels a sense of loneliness there, as he has lost many important people and the village constantly reminds him of those losses.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.
One possible reason could be that Hermione wants to pursue her own independent magical research. She is highly intelligent and may feel the need to focus on her studies without the distractions that come with being close to Harry. Another reason might be a disagreement over some major decision in the wizarding world. For example, if Harry has a different stance on how to deal with the remaining Death Eaters or how to reform Hogwarts' curriculum, Hermione, with her strong opinions, may choose to distance herself to avoid constant conflict.
One possible reason could be fear. Minato is a very powerful shinobi, and Naruto might be scared of him for some reason. Maybe he has heard stories about Minato that made him afraid.
It could also be due to a particularly bad encounter with someone in the village. For instance, if he was bullied severely by some older kids and he felt that there was no one to protect him. He might have thought that running away was his only option to avoid further harm.
He could become stronger on his own. Away from his family, he'll have to rely solely on himself. This self - reliance might push him to train harder and unlock even more of his 'godlike' powers. For instance, he might find new mentors or training methods that his family would not have allowed.
One consequence could be that his friends worry about him a great deal. They might go on a search for him, which could put them in danger as well. After all, they care about Naruto deeply and won't just let him disappear without trying to find him.
He might become more self - reliant. Without the immediate support of his family, Naruto has to learn to fend for himself. This could lead to a toughening of his character and a more independent mindset.
Maybe he's running away from some kind of danger or threat in his home village. There could be a group or an individual after him, and he believes that Kumo would be a safer place. It could also be related to some political unrest in Konoha that makes him feel like he has to leave, and Kumo seems like a viable option.
Perhaps he is running away from danger in Konoha. There could be a threat that he believes he can't face directly in the village, and he thinks Whirlpool might offer some sort of sanctuary or a way to become stronger in relative safety.