A major consequence is how other characters react. The village elders might treat him differently, perhaps with more reverence or more suspicion. Also, his enemies might see him as an even greater threat. Naruto himself might also feel a greater sense of responsibility towards the village, as he is now connected to its founder in a very special way. This could lead to him making different decisions in battles and in the overall story arc.
Yes, in some fanfictions, Naruto is depicted as the First Hokage's reincarnation. This often adds an interesting twist to the story, as it can bring in new relationships and powers related to the First Hokage's legacy.
One consequence could be a change in his relationships. For instance, his bond with Sasuke might be seen in a new light as it could be related to the Indra - Asura cycle. Another consequence is that his power might be explained in a different way, perhaps as an inheritance from Indra.
He would likely be seen as a traitor by the village. The villagers, who once saw Naruto as a hero - in - the - making, would now turn against him. He'd be hunted by the ninja forces of Konoha.
The implications are vast. In terms of international relations, Naruto as the 1st Hokage might make the Hidden Leaf more open to other villages right from the beginning. His reputation for kindness and his willingness to forgive could lead to better diplomatic relations. Moreover, the training and education system in the village could be revolutionized. He might focus more on individual growth and moral values rather than just pure combat skills, which would produce a different kind of ninja compared to what we see in the original Naruto story.
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.
If Naruto changes something major in the past, it could disrupt the timeline. For example, if he prevents the Uchiha massacre, Sasuke's path would be completely different. He might not have the same drive for revenge, which could mean he doesn't leave Konoha. This would change Naruto's own growth as a ninja, as Sasuke was a big part of his motivation to get stronger.
The village's morale could take a huge hit. Naruto is a symbol of hope and strength. If he jumps off the monument, it would make the villagers question their own safety and the stability of the village. Politically, it could cause unrest as the village leaders would have to deal with the aftermath and try to keep the situation under control.
One advantage is having great power. As the Hokage, you can lead the village, make important decisions, and protect your people. You get to use powerful jutsu and have a high status in the ninja world.
One implication is new power - ups for Naruto. He might gain abilities related to Hamura's ocular powers or his connection to the moon.
In fanfiction, if Naruto is the reincarnation of Minato, it could mean a stronger bond with the Uzumaki clan. Since Minato was an important part of the clan through his marriage to Kushina. Naruto could have access to hidden Uzumaki knowledge or powers more easily. Also, his relationships with characters like Jiraiya could be different. Jiraiya trained Minato, and if Naruto is his reincarnation, Jiraiya might see more of Minato in Naruto and train him in a more specialized way.