Perhaps Naruto jumps off the Hokage heads as part of a training exercise in the fanfiction. He might be testing his new skills, like a new form of chakra control or a new jutsu that allows him to land safely. It could also be a bet with his friends, like Sasuke or Sakura, to prove his courage and abilities.
On the positive side, it could boost his reputation among some of the younger ninja. They might see him as a fearless and rebellious figure. However, it could also create a divide in the village. Some would admire his boldness while others would condemn his actions as reckless and irresponsible.
He could get seriously injured. The Hokage monument is very tall, and the fall would be a long one. Naruto might break his bones or worse.
One possible plot could be that Naruto is facing extreme self - doubt. Maybe he feels he has failed the village in some way, like not being able to prevent a major disaster. So, in a moment of despair, he jumps off Hokage Mountain. But then, his friends sense something is wrong and come to his rescue just in time. They then have heart - to - heart talks with him and help him regain his confidence.
In some fanfiction scenarios, Naruto might jump off the Hokage monument to follow someone or something. For example, if there is a mysterious figure or a spiritual entity that he believes he needs to follow, and the only way seems to be by jumping. It could also be a symbolic act of breaking free from the expectations that come with being associated with the Hokage monument.
In some fanfictions, Naruto might jump in front of Sasuke during an emotional moment. For example, if Sasuke is about to make a rash decision that could put his life in danger, Naruto jumps in front to stop him and talk some sense into him. Naruto's presence in front of Sasuke could also symbolize his unwavering loyalty and friendship towards Sasuke, showing that he'll always be there for him no matter what.
One possibility could be that Peter is extremely stressed at school. Maybe he's being bullied or facing overwhelming academic pressure. So, in a moment of despair, he jumps off the school roof. But then, he could miraculously survive and this event could be a turning point for him to face his problems and seek help.
Sakura would be extremely distraught. She has always cared deeply for Naruto, and seeing him in such a dangerous situation would make her rush to his aid immediately. She might use her medical ninjutsu to heal him if he's injured. Kakashi, on the other hand, would be shocked but also proud that Naruto has the courage to face his inner demons in such a drastic way. He would try to understand Naruto's motives and help him get back on track.
Well, it could be about Naruto going on a journey to the west in search of new jutsu or to help a village there. Maybe he meets new characters and has to face different kinds of challenges that are unique to the western regions in the Naruto universe.
Maybe Kakashi. He's been Naruto's teacher and mentor. He has the skills and the loyalty to Naruto. He could use his Lightning Blade technique to quickly reach Naruto during the fall and carry him to safety.
One possible plot could be that Naruto is somehow transported to a different timeline where he has to fight the Hokage for a misunderstanding. Maybe there's a villain who has manipulated events to make the Hokage think Naruto is a threat. So Naruto has to fight not only to prove his innocence but also to save the village from the real danger that the villain poses.