Perhaps he's following a lead related to his parents. There could be some secrets about his family that are hidden in America. He goes there to uncover the truth and learn more about his family's past that might not be available in the UK.
Well, perhaps it's about control. The 'Harry Potter' franchise is a huge brand. By leaving fanfiction, it can better control the narrative and the way the story is perceived. Fanfiction can sometimes deviate greatly from the original intention, and this might not be in line with the long - term vision for the 'Harry Potter' brand. It could also be that they want to distance themselves from some of the more controversial or inappropriate fan - created content that may exist in the fanfiction realm.
In some fanfictions, Harry might leave because of Ginny due to a misunderstanding. For example, he could misinterpret Ginny's actions or words as a sign that she no longer loves him or wants him around. This could be something as simple as seeing her chatting happily with another guy and jumping to the wrong conclusion.
One reason could be to escape the constant reminders of his past traumas in Britain. The place is filled with memories of Voldemort and the battles he fought. Maybe in the fanfiction, he just wants a fresh start away from all that chaos and danger.
Well, it could be that the author wants to show Harry's perseverance and growth through constantly dealing with unwanted attention. It makes his character stronger.
One possible reason could be that he feels constantly in danger at Hogwarts. With all the dark magic threats and attacks that keep happening, he might think leaving would keep his friends and himself safer. For example, after the Chamber of Secrets incident, he might have considered leaving to protect others from Voldemort's influence.
He could be disillusioned with the wizarding world's politics and power struggles. So, taking his money and leaving is his way of getting away from it all. He might feel that he can't make a real difference within the existing system and decides to find his own path.
Perhaps he gets a chance to attend a special magical school or training program that requires him to leave the Dursleys. It could be a place where he can develop his powers without the Dursleys' interference. Also, he may be running away from a threat that the Dursleys are unable or unwilling to protect him from.
One reason could be that he's tired of the constant danger and battles. After all he's been through, he might just want a normal, peaceful life away from magic. Maybe he wants to start a family in the Muggle world where his kids can grow up without the threat of dark wizards.