In the fanfic, Naruto could hate the Hokage because of some bad experiences related to past Hokages. Perhaps he discovers some dark secrets about how the Hokage office has made decisions that he doesn't agree with. It might be something like a cover - up of certain events that Naruto believes should have been dealt with more fairly.
In the main Naruto story, the Hokage is seen as a protector and a symbol of hope for the village. In the fanfic where Naruto hates the Hokage, it goes against this core concept. It might lead to different relationships between Naruto and other characters who are associated with the Hokage. For instance, he might have a strained relationship with the current Hokage or those who support the Hokage system, which is very different from how he interacts with them in the original story.
Perhaps Naruto feels that the Hokage has been too strict or unfair in dealing with certain situations. Like if the Hokage didn't support Naruto's way of trying to bring peace and unity, which Naruto firmly believes in. This could lead to a growing resentment and eventually hatred.
Shikamaru is another possibility. He is known for his strategic mind. As Hokage, he could use his intelligence to make wise decisions for the village. He may not have the brute strength of Naruto or Sasuke, but his ability to plan and analyze situations would be invaluable in leading Konoha.
Well, in the original storyline, Naruto has great respect for the Hokage. He dreams of becoming one himself. But in this fanfiction, the hatred is a complete contrast. It changes the fundamental relationship dynamics.
One possible reason could be the pressure associated with the Hokage title. Naruto has always been in the spotlight and being Hokage comes with a huge burden of responsibility. Maybe in the fanfiction, he resents how it restricts his freedom to just be himself and have adventures like he used to.
In the original story, Naruto always aspired to be Hokage. But in this fanfiction, his hatred is a complete deviation. It changes the fundamental motivation of his character.
Perhaps a perk is the ability to shape the future of the ninja world. As Hokage, one can inspire the younger generation of ninjas. They can create new ninja academies or training programs. They also have the power to pardon or punish ninjas according to their deeds, which helps in maintaining law and order in the village.
Sasuke could also be a possibility for the 6th Hokage in the fanfic. He has grown stronger over the years and his unique perspective on the ninja world could bring new ideas to the leadership of the Hidden Leaf. He might start off as a controversial choice but prove himself through his actions in protecting the village and making tough decisions.
It could be that in this fanfiction, Naruto has been influenced by some false information about the Fourth Hokage. Some villains might have spread lies about the Fourth Hokage's actions, and Naruto, being young and naive in the story, believes those lies and thus starts to hate the Fourth Hokage.