One possible consequence could be that Naruto grows up away from the influence of Konoha's shinobi culture. He might develop a different set of values and skills. For example, without the guidance of Iruka and Kakashi, his understanding of ninjutsu and teamwork could be very different. Also, his relationships with characters like Sasuke and Sakura would be greatly affected. Maybe he wouldn't have the same rivalry with Sasuke, and his bond with Sakura might not even form.
Naruto's character development would likely be more influenced by Kushina's values. He might be more empathetic towards certain things that Kushina cared about. For example, if Kushina had strong feelings about a particular clan or group, Naruto could grow up with a similar mindset.
Well, one possibility could be that Kushina takes Naruto away to protect him from the dangerous world of shinobi. Maybe she wants to raise him in a peaceful place away from the constant threats and battles in the Hidden Leaf Village.
One reason could be that he feels misunderstood by the villagers. Despite all he has done for Konoha, some still hold grudges or are afraid of his power. Another might be that he wants to explore the world on his own terms, away from the responsibilities and restrictions of Konoha. Maybe he also feels a sense of loneliness there, as he has lost many important people and the village constantly reminds him of those losses.
Perhaps Naruto feels that Kushina is being overprotective. He wants to prove his independence and go on his own adventures without her constant supervision, so he decides to run away.
There might also be other characters involved. For example, Minato might make an appearance in flashbacks. Since he was Kushina's husband and Naruto's father, his presence could be important in terms of the backstory. Also, characters from the Hidden Leaf Village might be mentioned or even try to find Naruto and Kushina, like Iruka Sensei who has a special bond with Naruto.
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 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.
He might face a lot of danger on his own. Since he's running away from Kushina who would usually protect him, he could encounter stronger enemies that he's not fully prepared to face.
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.