Maybe it's because a lot of Naruto fanfiction has become very clichéd. There are always the same overused plotlines, like the main character being an overpowered self - insert. People get tired of reading the same thing over and over again.
Authors should focus on creating unique and original plots. Instead of relying on the same old tropes, they could explore different aspects of the Naruto world, such as the backstories of minor characters. This would make the fanfiction more interesting.
Perhaps Naruto feels that Kushina is being overprotective. He wants to prove his independence and go on his own adventures without her constant supervision, so he decides to run away.
He might miss out on some crucial training. Jiraiya has a lot of knowledge and skills to pass on, and by running away, Naruto could fall behind in his development as a ninja.
One possible reason could be that Naruto might be afraid of the intense training Jiraiya has in store for him. Jiraiya is known for his strict and grueling training methods, and Naruto, being young and sometimes impatient, might just want to escape that for a while.
In a 'Percy Jackson Walks Away' fanfiction, he could be walking away due to a falling - out with his friends. Maybe there was a misunderstanding about a quest, and he feels betrayed. He leaves to prove himself on his own terms, without relying on his usual group of allies.
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.
One possible reason could be a growing difference in their life goals. Hermione is highly ambitious and focused on her studies and making a difference in the wizarding world. If Ron is more laid - back and not as driven in the fanfic, it might lead to Hermione walking away. For example, she might be constantly frustrated with his lack of initiative in certain important matters.
Maybe he feels misunderstood by his family. In many Naruto stories, his family situation can be complex. If he's 'godlike', he might have powers that his family doesn't understand or fears, leading him to run away to avoid conflict or being treated differently.
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.