It depends on the specific fanfic. Some authors might come up with this plot twist to explore different character motivations and conflicts. In others, it might not be the case at all.
The main challenges would likely be navigating Danzo's complex web of intentions. Plus, they'd have to adapt to a training style that might push their limits and deal with the potential backlash from the rest of the village for working with Danzo.
One reason could be Sasuke's thirst for power. If he believes Naruto is the only obstacle in his path to ultimate power, he might be driven to kill him. In some fanfictions, Sasuke may be influenced by a dark entity that twists his mind into thinking Naruto is a threat that needs to be eliminated.
One possible reason could be that Sasuke might have gone too far in his pursuit of power even after the war. He could have been a threat to the newfound peace in the ninja world, and Naruto, as the protector of peace, might have felt he had no other choice.
If in a Sasuke fanfic, one possible reason could be unrequited love. If Sakura feels that Sasuke will never return her love and she has exhausted all hope, she might sink into despair. Another reason could be if she feels she has failed Sasuke in some way, like not being able to protect him or help him in his goals. Maybe she blames herself for his continued pain or suffering and sees no way out but to end her own life.
It could also be a completely new character introduced into the fanfiction. A foreign ninja who was inspired by some of Danzo's ideas (not the bad ones) and comes to Konoha to take on the role of successor, bringing in new perspectives and ways of doing things.
One reason could be to create shock value. By having two main characters kill another important character, it grabs the reader's attention. Another could be to explore a very dark and alternate version of the Naruto universe. Maybe the writer wants to show how far characters could be pushed in extreme situations.
Perhaps in a fanfiction, Sasuke discovers a new and extremely dangerous power that he can't control and it starts to endanger Konoha. Naruto tries to stop him but in the heat of the battle, accidentally kills him. Overwhelmed with guilt and feeling that the village will never understand, Naruto leaves. But this is a very different take on their relationship and the Naruto world as a whole.
One idea could be a crossover where Naruto and Sasuke are somehow transported to the world of Akame ga Kill. They could team up with Akame and the Night Raid members to fight against the corrupt empire in that world. Maybe Naruto uses his shadow clones to gather intelligence, while Sasuke's sharingan helps in combat against the powerful foes.