It could be due to the current situation in the village. There might be threats that required Naruto to stay. Tsunade, as the Hokage, had to consider the overall safety and stability of the village. So, she denied Naruto's request for the training trip to ensure he was available in case of any emergency.
In such a fanfic, Sakura could learn advanced medical ninjutsu from Tsunade. Tsunade, being a master in the field, would likely push Sakura to her limits. Maybe Sakura would also gain more physical strength training under Tsunade, like learning to break boulders with her bare hands as Tsunade can.
Tsunade would likely use physical conditioning methods. She might have Naruto run long distances while carrying heavy weights, similar to the training she did herself to build her strength. This would improve his stamina and overall physical strength for battles.
We can expect Sakura to grow as a ninja. Tsunade is a tough teacher, so Sakura would become more disciplined. For example, she would have to wake up early and train all day long.
There might be a fanfiction where they are all involved in a medical emergency. Since Tsunade is a great medical ninja and Sakura is her apprentice, and Naruto is always in the thick of things. They have to work together to save a village from a mysterious illness. It would be full of drama and moments of them relying on each other's skills.
A possible plotline could be a training arc. Tsunade could be training both Naruto and Sakura in a new and advanced form of combat or medical ninjutsu. This would involve a lot of character development as they struggle to master the new skills. For example, Naruto might have trouble with the precision required in a medical - related technique while Sakura helps him out, and Tsunade observes and gives tough love guidance.
The plot could involve a mystery in the village. Strange things start happening, and Naruto, Sakura, and Tsunade have to work together to solve it. Along the way, they face various challenges, and their individual skills and teamwork are put to the test. They also learn more about each other's pasts and how it relates to the current mystery.
There are also fanfics where they team up for a long - term project, like rebuilding a village. In this scenario, Naruto could be in charge of motivating the villagers, Sakura would handle the medical and logistical aspects related to the villagers' well - being, and Tsunade would oversee the overall construction and security of the village. This kind of fanfic really shows their different strengths and how well they can work as a team.
Another type could be alternate universe fanfics. Picture a world where Naruto, Sakura, and Tsunade are part of a different ninja clan structure. They might have different roles and abilities in this new setting, and the fanfic could explore how they adapt and interact within this changed Naruto - like world.
I think all three are great in their own ways. Naruto is the heart of the story, his optimism and determination are infectious. Sakura has the potential to be a complex and strong female character. She can have her own character arc that is independent yet related to Naruto and Tsunade. Tsunade, with her long history and powerful abilities, can be a source of both conflict and resolution in the fanfictions. For example, her past experiences can create interesting plot twists when combined with the current situations of Sakura and Naruto.