One possible reason could be for his safety. Konoha is a well - protected village with many skilled ninja. She might believe that leaving him there would ensure he has the best chance at survival and growth as a ninja. Also, she may have some mission or obligation that forces her to leave him behind, perhaps something related to the greater good of the village or the ninja world in general.
Naruto would probably feel abandoned at first. He might become more withdrawn and have trust issues. But as time goes on, he could grow stronger out of a need to prove himself. He may also form closer bonds with his friends in Konoha, like Sasuke and Sakura, as they become his new family in a way.
Well, if Naruto and Kushina left Konoha in fanfiction, it would change a great deal. Naruto would not have the same relationships with his friends like Sasuke and Sakura. He might develop different fighting styles as he wouldn't be trained by the same people in Konoha. Kushina, being a strong kunoichi, could train Naruto in her own unique ways. And their departure could also cause a stir in Konoha, with some people trying to find them and others realizing the mistakes they made in how they treated Naruto and his family in the past.
One possible reason could be for Naruto's safety. Maybe she has to go on a dangerous mission and believes Konoha is the safest place for him. Another reason might be that she is forced by some powerful enemies who threaten Naruto's life if she doesn't leave him in Konoha.
The plot could develop in various ways. For one, Naruto's power growth might accelerate as he and Kushina explore different regions and learn new techniques. They could also encounter old enemies of the Uzumaki clan, which would add a new layer of conflict. Maybe they'd find a lost Uzumaki village and help revive it.
They might leave because of a prophecy. If there was a prophecy that Naruto would bring destruction to Konoha or that Konoha would bring destruction to Naruto, Kushina might take Naruto away to prevent it.
In a 'naruto and kushina leaves konoha fanfic', perhaps they leave due to a threat to Naruto's safety that the village can't fully protect against. Maybe some secret organization is after him and they feel they have no choice but to go into hiding outside Konoha.
The relationship between Konoha and the Uzumaki clan might be further strained. With Kushina leaving, Konoha would lose an important link to the Uzumaki. And other Uzumaki members might see this as a sign that Konoha is not a safe place for them.
In Naruto fanfiction, a Kushina mind - wipe in Konoha could lead to some really interesting plot twists. Maybe it could be part of a scheme by an enemy to disrupt Naruto's life further. Since Kushina was Naruto's mother, her having a mind - wipe would change the dynamics of how Naruto discovers his family history and heritage.
The first consequence could be a breakdown in the village's unity. Naruto is seen as a hero in Konoha, and if he turns against it, many of his supporters might be confused or even follow his lead. This could lead to internal strife within the village.