In this type of fanfiction, Naruto leaving Team 7 can be a very emotional and plot - twisting scenario. It might lead to Hinata stepping up to support Naruto in different ways. For example, she could be the one to convince him to come back to the team eventually. Also, this situation can explore the deeper feelings between Naruto and Hinata as they are forced to deal with the change in their dynamic.
Sasuke might become more withdrawn. He was always in a sort of rivalry with Naruto, and without Naruto there, he could lose some of his motivation to get stronger. Sakura would be devastated. She cared about Naruto, and his leaving would make her question what went wrong. Kakashi would also feel a sense of failure as a teacher.
When Naruto leaves Team 7 in this Naruhina fanfic, it could set off a chain of events. Hinata might start training harder to be strong enough to support Naruto. Their interactions could involve Hinata sharing her own insecurities with Naruto, which makes him see her in a new light. This mutual sharing and support can be the foundation for a deeper Naruhina relationship, while also dealing with the consequences of Naruto's departure from the team.
One possible scenario could be that Naruto leaves due to a misunderstanding with Sasuke. Maybe Sasuke says something harsh about Naruto's skills and Naruto, in his pride, decides to leave. Another could be that Naruto feels he's holding the team back in some way and leaves to train on his own in order to become stronger without being a burden. Or perhaps there's a mission gone wrong where Naruto is blamed for something he didn't do, and he leaves out of a sense of unfairness.
Sasuke might initially be indifferent on the surface, but deep down he would feel a sense of loss. He has always had a rivalry with Naruto, and Naruto's departure would mean an end to that dynamic. Sakura would be devastated. She has grown to care about Naruto as a friend and teammate, and his leaving would leave a big hole in the team.
One possible plot development could be Naruto leaving due to a misunderstanding. For example, if he is wrongly accused of a crime within the team. Another could be that he feels he is holding the team back in some way and decides to leave on his own to become stronger alone. Maybe he has a personal goal that he believes he can't achieve while still being part of Team 7.
One reason could be to explore Sakura's character development outside of the traditional Team 7 dynamic. By having her separated from the team, it allows the writer to focus on her individual strengths and weaknesses.
The scenario where Team 8 saves Team 7 instead would be quite interesting. It could introduce new conflicts and resolutions, and potentially reveal hidden strengths of Team 8 that weren't previously showcased.
There's a fanfiction called 'Sakura's Battlefront' which is full of action. In it, Sakura and Team 7 are thrust into a war - torn land where they have to fight off waves of powerful enemies. Each member of the team gets to show off their combat skills in intense battles.