Sakura might be initially shocked but then understand Naruto's decision. She could secretly help them by providing medical supplies. Shikamaru, being the smart one, might predict their actions and try to cover for them so that the village doesn't find out too quickly.
Another reason could be related to a prophecy or a hidden mission. They might have learned about a prophecy that required them to leave Konoha in order to fulfill it. This could involve finding a powerful artifact or learning a special technique that could only be achieved by being away from the village. Their departure would then be a sacrifice for the greater good of not just Konoha, but the entire ninja world.
One possible plot could be that they run away to avoid a political marriage arranged for Naruto. They find a peaceful, hidden village where they start a new life. Naruto uses his skills to hunt and Hinata uses her Byakugan to forage for food and keep watch for any potential threats.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
From a security perspective, Konoha would be weaker. Naruto is a very powerful ninja, and Hinata is no slouch either. Their skills and abilities would be missed. Enemies might see this as an opportunity to attack Konoha. Also, Naruto has been a symbol of hope for the village. His departure could lead to a decrease in morale among the villagers. They might start to feel less secure and more pessimistic about the future.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.
They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
Perhaps Naruto discovers something about Itachi that the rest of the world doesn't know and he needs to run away to protect that secret. It could be a powerful jutsu or a message that could change the balance of power in the ninja world.
Maybe they run away to avoid an arranged marriage. Sakura, being strong - willed, leads the group. Ino could use her mind - transfer jutsu to gather information on safe places to hide. Hinata is there for her gentle support, and Tenten provides her weapon - skills for protection. They end up in a hidden valley where they train in secret.