Maybe in the fanfiction, his excessive pride got in the way. He was so confident in his military might from his past victories that he underestimated the threats within his own kingdom. This led him to be complacent, and when the challenges arose, he was ill - equipped to handle them.
Often, they are portrayed as outcasts trying to find their place. They may be angry at the world for their status.
It could be a really wild and unexpected crossover. Maybe Harry would have a penchant for the political intrigue and power plays of Game of Thrones.
Some of the secondary characters could include those who interact with the bastards. It could be a mentor figure, an old knight who takes one of the bastards under his wing and teaches him the ways of war and honor. Or it could be a love interest, a noble lady who falls for one of the bastards despite the social barriers, adding a romantic sub - plot to the story.
One interesting plotline could be a bastard of Robert's rising to power in a unexpected way. Maybe he uses his knowledge of the Baratheon family secrets to gain influence. For example, he could expose some hidden affairs or deals that the main families were involved in, which would shake the power dynamics in Westeros.
One possible fanfiction could start with Robert Baratheon as a young man. He is full of ambition and dreams of a united Westeros under his rule. He trains hard in combat, his sword becoming an extension of himself. He meets his future friends, like Ned Stark, during these formative years. They share tales around the campfire and make grand plans for the future. As he grows older, he participates in battles, his victories making him more and more renowned. His charisma draws people to him, and soon he is seen as a natural leader. But with power also comes temptation, and he has to face the challenges of politics and intrigue that come his way.
One possible plot could be the bastards uniting to claim a part of the Iron Throne. They might form an alliance based on their shared blood and the injustice they've faced. Another could be a single bastard's journey to discover his true identity and his place in the chaotic world of Westeros.
One idea could be a fanfiction where Robert Baratheon's son, perhaps Joffrey (even though he was a cruel character), has a change of heart. In this fanfic, he could start to see the error of his ways after meeting a wise old maester who tells him tales of great but just kings. He then tries to make amends for his past actions, which would be a huge departure from his original character arc in the show and books.
She could also be shown as a great warrior in certain fanfictions. Despite the norms of the society in Game of Thrones that often restrict women's roles in combat, she breaks free from those constraints. She trains in secret and then emerges as a surprise defender of her family when they are under attack.
One possible alternate storyline could be that Robert manages to uncover the truth about Cersei's infidelity earlier. This would lead to a major political upheaval in King's Landing. He might exile Cersei and her children, which would change the power dynamics completely. With no Lannister influence at court, Ned Stark might have more sway, and the events leading to the War of the Five Kings could be averted.
One possible plot could be that their son discovers the truth about his parents' tumultuous relationship. He might struggle with the knowledge that his mother had affairs and his father was not the ideal man he seemed. This could lead him on a journey of self - discovery, trying to figure out his place in the Seven Kingdoms.