Maybe the filmmakers wanted to focus more on the current adventures of Spider-Man rather than going back to the origin. It could be a creative choice to give a fresh take.
In the 'Spider - Man Web of Shadows' story, Spider - Man is at the center. His love interest Mary Jane plays a significant role. Other characters include his fellow superheroes. For instance, Luke Cage, who has his own unique abilities and can be a powerful ally or an adversary depending on the situation. Wolverine also makes an appearance. His healing factor and his ferocious fighting style add an interesting dynamic to the story. There are also the villains who are either behind the symbiote invasion or are part of the chaos it causes.
A fanfiction could focus on Black Cat's backstory within the Web of Shadows context. Maybe she has a secret past connection to the symbiotes that is slowly revealed as she battles against them. This would add depth to her character and her role in the story.