In some fanfics, there could be a plot twist where the Wizengamot itself is under the influence of a spell. So, the whole trial is a setup not just for Harry but for a larger scheme to undermine the Ministry of Magic. This would mean that Harry has to not only prove his innocence but also expose the real threat to the wizarding world.
Obviously, Harry Potter himself is one of the most common. Then there's Dumbledore who often plays a role, either as a supporter or as someone with a complex plan. Hermione is also common as she uses her intelligence to help Harry in the trial.
Well, in some fanfictions, a plot twist could be that a character thought to be on Harry's side in the Wizengamot trial actually has a hidden agenda. Maybe they are being blackmailed by Voldemort's supporters. Also, it could be that the magical creatures of Hogwarts, like the house - elves, come forward with evidence that no one expected, which completely turns the trial around. For example, they might have witnessed something crucial that the wizards overlooked.
He might face political intrigue. There are likely those in the Wizengamot who oppose him due to his past actions and his association with Dumbledore. Also, he has to deal with the complex and often archaic laws and traditions of the wizarding world which could be a huge obstacle.
Well, in some fanfictions, Harry might gain control over the Wizengamot through his heroic deeds. For example, if he saves the wizarding world from a great threat again, the public support could be so strong that he can influence the Wizengamot's decisions. He could also use his knowledge of magic, especially some ancient or powerful magic that gives him an edge in the political arena of the wizarding world.
They are often portrayed as the villains. Their years of treating Harry badly are brought to light. They might look scared and out of place in the wizarding courtroom, with all its strange sights and magic.
There are fanfics where the Wizengamot is reformed by Hermione. In these stories, she uses her intelligence and knowledge of the law to make the Wizengamot more just. This often involves her facing a lot of opposition from the old - guard pure - bloods who want to keep things as they are. It makes for a great story as it combines Hermione's character traits with the complex political structure of the wizarding world.
They're popular because the Wizengamot in the original 'Harry Potter' series is often seen as a symbol of the old - fashioned and sometimes unjust wizarding government. Fanfiction writers like to explore the idea of challenging this authority. It gives a sense of empowerment to the characters and readers alike.