Another possibility is that Naruto wears the mask as a tribute to Kakashi after a significant event. It could be that Kakashi sacrifices himself to save Naruto and the village. So, Naruto dons the mask to carry on Kakashi's legacy and to always remember the lessons he learned from him.
If it's a more spiritual fanfiction, the mask could have a connection to the spirit world. Naruto wearing the mask could open a portal to that world or allow him to communicate with the spirits of past ninjas. He could then seek advice from the great ninjas of the past through the power of the mask.
It could also be a form of self - protection. Wearing a mask might shield her emotions. Sakura has been through a lot, and like Kakashi, who may use the mask to hide his past traumas, she might be doing the same. For example, if she's trying to distance herself from her old self or past relationships that have caused her pain.
The mask could make her look more like a lone wolf, similar to how Kakashi often gives off that vibe. Others might assume she has some hidden motives or a new, more secretive side to her. It might also attract different kinds of attention. Some might be intrigued by the new look and try to figure out why she's wearing it, while others might be a bit put off by the change as it goes against the more open and friendly image they had of her before.
Perhaps in this fanfiction, Sakura wearing the mask - like Kakashi is a symbol of her growth. She might be emulating Kakashi's calm and collected demeanor. It could start with her being inspired by Kakashi's success in various missions. So, she decides to wear a similar mask to see if she can also gain an edge in her own missions, both in terms of physical combat and mental strategy.
It could be Orochimaru. He has always been a major threat in the Naruto universe. If Sakura is on a mission while wearing the mask - like Kakashi, Orochimaru might be interested in her new look or the power she seems to be emulating. He could try to capture her to study her abilities or use her for his own evil purposes.
He might become more reserved. Kakashi is often a bit aloof and mysterious, and wearing the face mask like him could make Naruto act in a more subdued way, not showing his emotions as openly as he usually does.
Perhaps in this fanfiction, there's a specific mission or situation. Maybe they are on a stealth mission together, and Naruto decides to wear a face mask like Kakashi to blend in better or to follow some kind of ninja code that Kakashi has taught him for this particular task.
People like it because it offers a different take on the Naruto universe. Kakashi and Sakura have a unique dynamic in the original series, and fanfiction allows for exploring a romantic relationship that wasn't fully developed in the anime or manga.
In the "Mortal Cultivation Biography", when Han Li joined the Drifting Cloud Sect, he had to wear a mask to conceal his face due to his cultivation of the Eternal Spring Arts. As such, he wore a silver ghost mask.
While waiting for the TV series, he could also click on the link below to read the classic original work of " The Legend of Mortal Cultivation "!