One possible reason could be the trauma he has faced. Harry has endured a great deal of pain, from the loss of his parents to the constant battles and threats in the wizarding world. He might want to escape all that and find peace away from it.
One possible reason could be that in some fanfics, the author wants to explore a different side of Harry. Maybe he's tired of the constant chaos and danger in the wizarding world. Another reason might be to show his independence from the typical wizarding narrative. He could be seeking a more normal life away from all the magic and politics.
The plot could start with Harry making a firm decision to leave. He might go into hiding in the Muggle world, changing his appearance and identity. Then, the wizarding world would gradually realize his absence and start to search for him, which could lead to a cat - and - mouse chase.
It could be that in the fanfic, Harry Potter discovers some deep - seated secrets about the wizarding world's power structure. Feeling betrayed, he decides to take extreme actions to expose and destroy it. For example, if he finds out that the Ministry of Magic has been using unethical means to control the wizarding population, he might use his influence and magic to bring it all crashing down. He could start by revealing the truth to the public, which could lead to chaos and the destruction of the established order in the wizarding world.
A 'Harry Potter World Traveler' fanfic can expand the wizarding world in multiple ways. Firstly, it can introduce new magical locations. Instead of just Hogwarts and Diagon Alley, we get to see enchanted cities in South America or hidden islands in the Pacific. Secondly, it can explore different forms of magic. There could be a type of magic based on music in some far - off land. And thirdly, it can bring in new characters from various parts of the world, each with their own backstories and motives.
It could be about Harry Potter achieving ultimate power and ruling the wizarding world. Maybe he overcomes new and even more dangerous dark forces and in the process, he becomes the king. He could make new laws and bring about great changes to Hogwarts and the entire wizarding community.
Obviously, Harry Potter himself. Hermione and Ron would most likely be there too, as his closest friends. Dumbledore might still play a role, perhaps as an advisor to Harry in his new position. And there could be new characters, like wizards and witches from other parts of the world who come to see the new king.
One possible reason could be that he's tired of the constant danger and politics in the wizarding world. After all he's been through so much. He might just want a normal, quiet life away from magic.
One possible reason could be extreme anger. If something really bad happened to his loved ones, like if Voldemort came back in a different way and killed all his friends and family this time, Harry might be driven to the edge and decide to destroy the wizarding world that couldn't protect them.
They expand it by exploring the teachers' personal lives. For example, a fanfic might show Professor Trelawney's family history and how it affects her divination skills. This adds depth to the world.