One possible storyline could be that Izuku discovers a different quirk within himself. Maybe a latent quirk that was overshadowed by his admiration for All Might and One for All. For example, he could have a quirk related to intelligence amplification, which would make him a brilliant strategist in hero battles.
Perhaps Goku would form a different kind of bond with his friends. Instead of a marital relationship with Chichi, he might develop a closer brother - like relationship with Krillin. They could go on adventures together, not having to worry about family responsibilities. Goku could also focus more on mentoring younger fighters, like Gohan, in a more detached way, as a master rather than a father.
Another possibility is that he joins a different hero school. Maybe there's a smaller, more specialized school that focuses on a particular aspect of heroism that UA doesn't. For example, a school that specializes in rescue operations could be a great fit for Izuku's empathetic nature.
His relationship with All Might would be very different. Instead of being a successor, he might become more of a protege in a general sense. All Might could still mentor him, but their bond wouldn't be centered around One for All.
One reason could be fear. The life of a hero is full of danger. Izuku might have seen the toll it takes on heroes, like All Might's weakened state. He could be afraid of getting seriously injured or even dying. Another reason might be self - doubt. Despite his initial dreams, he may have come to believe that he doesn't have what it takes to be a great hero, in terms of both physical and mental strength.
One possible plot could be that Izuku, under All for One's influence, has a completely different view of hero society. He might be trained in unique and perhaps unethical ways, leading to a conflict within himself as he tries to figure out his own identity and what it means to be a 'hero' or a 'villain'.
If All For One kidnaps Izuku in fanfiction, Izuku's friends would surely try to rescue him. They could form a plan, with Bakugo being especially determined as he has a long - standing relationship with Izuku. All Might might also get involved, using his remaining power to try and save his successor.
Well, he may also have some emotional encounters. Maybe he'll have heart - to - heart conversations with the past users' consciousness within One For All. This could help him better understand the true nature of the power and the great responsibility that comes with it.
One possible storyline could be that Naruto decides to focus on traveling the world instead of becoming Hokage. He could use his skills to help people on a more individual basis across different villages. He might learn new jutsu from various shinobi cultures and become a sort of wandering hero.
One possible storyline could be that Harry is sorted into a different house than Gryffindor and thus doesn't cross paths with Ron as much. He might form closer relationships with students from his new house, like Hufflepuff or Ravenclaw. This would lead to a whole new set of adventures and friendships for Harry that don't involve Ron at all.
One possible storyline could be that Naruto has faced so many disappointments that he decides to isolate himself from the Hidden Leaf Village. Maybe he feels betrayed by the people he once trusted, like some of the village elders. He might then embark on a journey alone, exploring new lands and meeting different shinobi cultures.