naruto proved he is minato's grandson

Naruto's character would develop in a more balanced way. Minato was calm and intelligent. So Naruto would learn those traits from him. He wouldn't have the same insecurities as in the original story. He might be more of a natural leader from the start, as Minato was also a respected leader. And he would have a better understanding of the village's politics and history because Minato would be there to educate him.

Minato could be developed further by exploring his time as the Fourth Hokage more deeply. For example, show his political decisions and how they were influenced by the presence of the Kyuubi. Also, his relationship with other villages could be explored, especially in relation to the Kyuubi's power. Maybe he had to make some tough calls to protect the village from those who might want to use the Kyuubi for evil.

Yes, there might be such fanfictions out there. Fanfiction writers often come up with creative and unexpected relationships between characters. They like to explore different 'what - if' scenarios. So, it's not surprising that someone could write a story where Naruto has a relation to Hanzo as his grandson.

He'd become more mature. Knowing Minato's experiences would make him see the ninja world from a different perspective.

Well, it depends on the specific fanfic. Some fanfics might really emphasize Naruto's growth to be on par with Minato in terms of smarts. They could show Naruto learning from Minato's memories or having some sort of spiritual connection that transfers knowledge. However, other fanfics might focus more on other aspects of Naruto's character and not necessarily make him as smart as Minato.

I recommend the novel "From the Leaf to the God" to you. The main character was called Uchiha Kirikyo, the grandson of Uchiha Kyo. He traveled through the Naruto World and awakened the placement system. By placing it in different locations, he could gain proficiency in ninjutsu and blood inheritance. After he became a Chuunin, he stayed in the secret department of the hospital for five years. His medical ninjutsu and creation and regeneration proficiency were maxed out. After his father passed away, he inherited his father's will, reformed the Yu Zhibo clan, and seized the power of Naruto. In the novel, the protagonist was Uchiha's grandson. I hope you like this fairy's recommendation. Muah ~😗

Naruto's powers would be a strange mix. He could inherit Orochimaru's ability to regenerate, but in a more Uzumaki - style way. His rasengan could be infused with snake venom or some sort of snake - based chakra. And he might be able to use Orochimaru's body - switching jutsu in a modified form, perhaps using it not for evil but for strategic purposes in battles.

Naruto would likely be more conflicted. He has always been an outcast in the village, but now with his relation to Madara, he would be even more of an enigma to the villagers. His character might become more brooding as he tries to understand his place in the world. He would still have his goal of becoming Hokage, but it would be colored by his new heritage. He might have to prove himself even more, not just to the village but also to himself that he's not like Madara in terms of causing chaos.

Their relationship was based on mutual respect. Minato respected Kushina's strength and determination, and Kushina respected Minato's skills and leadership qualities.

The relationship can be developed by having Minato appear in Naruto's memories more vividly. For example, Naruto could start having flashbacks of Minato's training sessions or family moments that he didn't know about before. This would make Naruto feel closer to his father.