It's popular because it creates an interesting dynamic. Snape has always had a complex relationship with Harry in the original series. When Harry is deaged, it gives Snape a chance to start anew and perhaps be a different kind of influence. It also allows for exploring Snape's more nurturing side which is a contrast to his usual cold persona.
One possible plot could be that Harry discovers a time - traveling accident has brought baby Snape to his present. Harry, being the kind - hearted person he is, takes it upon himself to care for the baby. He has to figure out how to feed the baby, keep him clean and comfortable. Maybe he also has to protect baby Snape from any threats in the wizarding world that might target Snape even as a baby.
Well, at first Harry might be very suspicious. But as Snape shows consistent care, Harry could start to see him in a new light. Maybe he realizes that Snape has more layers than he thought. He might begin to understand that Snape's past actions were more complex than just being mean to him.
Well, in such a fanfiction, it could greatly change the storyline. Snape is often portrayed as a complex and somewhat bitter character in the original story. But if he takes care of baby Harry, he might develop a different kind of bond with him. Maybe he'd become more protective and less resentful towards Harry as he watches him grow. This could lead to a completely different dynamic between Snape and the other characters too, like Dumbledore. He might not be as secretive from Dumbledore about his feelings for Harry.
There might be a fanfiction where Harry takes care of Snape after a battle. He could be the one to tend to Snape's wounds, both physical and emotional. Since Snape has always been a rather closed - off character, Harry's attempts to get through to him and provide care could be a great source of character development for both of them. Harry might use his Gryffindor courage to break down Snape's walls.
There could be a situation where Harry is being bullied by some students from other houses. Snape, despite his usual cold exterior, steps in and scolds the bullies. For Draco, if he gets into trouble with other Slytherins over some internal house politics, Snape would quietly resolve the issue. In addition, Snape might offer to tutor them personally. He would give Harry extra help with his Patronus charm, knowing its importance, and for Draco, he could teach him some advanced potions techniques that are not taught in regular classes.
Snape's care for his Slytherins can also be shown through his teaching methods. He may be strict, but in fanfiction, it's often with the intention of making them better. He could give extra tutoring to students who are struggling in potions or other subjects. He understands the Slytherin ambition and tries to channel it in a positive way, like encouraging them to pursue difficult but rewarding areas of magic study.
You can try looking on Archive of Our Own (AO3). It has a vast collection of Harry Potter fanfictions, and it's likely that you'll find several stories about Harry taking care of Snape there. Just use the search function and type in relevant keywords like 'Harry takes care of Snape' and you should get a list of relevant fics.
There's 'Snape and the Deaged Savior'. In this fanfiction, Snape discovers deaged Harry in an unexpected place. He takes on the role of caretaker with his usual grumpy exterior but deep down shows a lot of care. He teaches Harry magic in a different way than the normal Hogwarts curriculum, which makes for an interesting read.
Well, it could be about Snape feeling a sense of duty. Maybe after Harry loses his sight in a battle against the Dark Arts, Snape, despite their past differences, steps in. He might start by teaching Harry new ways to navigate Hogwarts using magic that doesn't rely on sight, like advanced sonar - like spells.