Maybe he wants to keep up with the latest news in the wizarding world. There could be important announcements, like news about Voldemort's activities or updates on the Ministry of Magic.
It could be that he's looking for information about his friends or Hogwarts. For example, if there are any articles about Quidditch matches at Hogwarts or news about Hermione's latest achievements in the field of magic study.
He might be interested in the articles about new magical creatures. Since he has had many encounters with different and often dangerous creatures, news about newly discovered ones or updates on known ones would surely catch his attention.
One reason could be defamation. If The Daily Prophet in the fanfiction spreads false and harmful rumors about Harry Potter, that might lead to a lawsuit. For example, if they wrongly accuse him of dark magic practices.
One interesting storyline could be about a young journalist at the Daily Prophet uncovering a long - hidden conspiracy within the wizarding world that involves some of the most prominent figures. It could add a new layer of mystery to the already rich Harry Potter universe.
They might have to issue a public apology. This is a common consequence when sued for something like false reporting. It would be a way to try and repair some of the damage done to Harry's reputation.
Hermione Granger is also very popular. In fanfiction related to the Daily Prophet, she might be working on a research project for the newspaper, using her vast knowledge to dig deep into important wizarding issues. Her intelligence and determination would shine through in this context.
Maybe Harry sues the Daily Prophet for spreading false rumors about him, like making up stories that he's secretly working for Voldemort again. It could be that these false reports are ruining his reputation and causing problems in his relationships at Hogwarts and in the wizarding community.
It could also be a strategic move. Gringotts is a highly secure place. By buying it, Harry could ensure the safety of important magical artifacts or secrets. He could use it as a base to store and protect things that are crucial for the future of the wizarding world, like ancient spells or prophecies.
Well, perhaps Harry is fed up with the false or malicious stories in the Daily Prophet in the fanfic and decides to take action to destroy it. Maybe he uses magic to burn all the copies or disrupt the printing process.
He might do it because the Daily Prophet has been printing untrue stories about him.
One interesting plot could be that the Daily Prophet reports on Harry and Ginny's adventures in the wizarding world post - Voldemort. Maybe they are on a mission to discover new magical creatures and the Prophet is covering their every move.