In fanfiction, sometimes the writers have their own interpretations. They could see Naruto's character in a way where his goals and dreams, like becoming Hokage, are so all - consuming that he simply doesn't have the emotional space to care about Sakura. His attention is diverted to more important things in his mind, such as protecting the village and his friends in a more general sense rather than having a special care for Sakura.
One challenge could be lack of experience. Naruto has no real family growing up and Sakura is young. They might struggle with basic things like feeding the baby at the right time. Another challenge could be dealing with the baby's crying. Naruto might get frustrated as he's used to action and not this kind of slow - paced, nurturing task. Sakura, while more patient, might still find it difficult when the baby won't stop crying and she can't figure out what's wrong.
One possible plotline could be that Sakura gets injured during a mission and Naruto takes it upon himself to nurse her back to health. He brings her food, makes sure she takes her medicine on time, and stays by her side to keep her spirits up. Another could be that Sakura is feeling down about her progress as a ninja, and Naruto encourages her and helps her train in a more patient and understanding way than she's used to.
One reason could be that it adds an interesting twist to the original Naruto - Sakura dynamic. In the canon, Naruto has strong feelings for Sakura for a long time. Changing this in fanfiction allows for new relationship developments, like exploring different pairings for Naruto without the complication of his unrequited love for Sakura.
Often, he might ignore her attempts to get his attention. For instance, in some fanfics, Sakura tries to talk to Naruto about something important, but he brushes her off like she's not important.
There's a fanfic where Sakura takes care of Naruto when he gets poisoned during a mission. She stays by his side day and night, making sure he recovers. It shows a very tender side of their relationship, and the author does a great job of portraying Sakura's determination to keep Naruto alive and well.
One possible plotline could be that Naruto gets seriously injured during a mission. Sasuke and Sakura, with their combined skills, take him in and nurse him back to health. They might have to deal with Naruto's stubbornness when it comes to resting and following medical advice. Sakura could use her medical knowledge, while Sasuke could provide protection and also train Naruto in new techniques once he's recovered a bit, strengthening their bond as friends.
It can change the focus of the story. Instead of having a love triangle or Naruto's pursuit of Sakura as a sub - plot, the plot can center more on Naruto's personal growth, his ninja training, or his relationships with other characters like Sasuke or Kakashi.
Sure. There's one where Sakura takes care of Naruto when he's in a coma after a near - death experience. She talks to him, tells him stories of their adventures together, hoping he'll wake up. It's a very emotional read.
Taking care of Naruto might make Sakura more empathetic. She has to understand Naruto's pain and needs, which could make her a better ninja overall. As for Sasuke, it could break down some of his walls. He has to be vulnerable in front of Naruto and Sakura, showing that he's not just the aloof and brooding ninja. This experience might also make him more open to the idea of relying on others and being part of a team again.