It could also be a way for fans to express their own feelings about the show. If they thought that the show was becoming too predictable with Rachel always in the Glee club, they write fanfictions where she leaves to add an element of surprise and freshness to the story.
Some people write it to explore different storylines that weren't explored in the original show. Maybe they felt that Rachel's character had more potential for growth outside of the Glee club, so they create fanfictions where she leaves.
People write it because they love the characters. Santana and Rachel are both complex and interesting characters in Glee. Their relationship in the show has its own tensions and chemistry, and fans like to explore different possibilities for them, like a kiss.
People write it because Snape is such a complex character. His leaving in the original story leaves a lot of room for speculation. Writers want to fill in the gaps about what he might do next, where he might go, and what his future holds.
In some fanfictions, Rachel leaves Glee to study music in a prestigious conservatory overseas. She has to adapt to a new culture, different teaching styles, and a whole new set of peers. It could show how she uses her Glee club experiences as a foundation while also evolving in this new and challenging setting.
Some write it to explore alternative storylines. Maybe they thought the original plot could have taken a different turn if Harry left at a certain point.
People like to write Rory leaves with Jess fanfiction because their relationship in the original show was full of potential. Many fans felt that they had a special connection that wasn't fully explored, so fanfiction allows them to create scenarios where Rory and Jess get a second chance at love.
They might write such fanfics to give Harry a new adventure. After all the events in the original books, his story doesn't have to end in Britain. It's a way to expand on his character and see how he would react in different situations outside his familiar homeland.
People write 'Thomas Leaves Sodor' fanfictions because they want to explore new storylines. The original setting of Sodor can be a bit limiting sometimes, so they send Thomas away to see what new adventures he can have.
They are a popular pairing because they are so different. Puck is the bad boy and Rachel is the over - achieving diva. Their contrast makes for interesting storylines where they can learn from each other.
It could also be for creative exploration. Writers might want to see how the storylines would change if these characters were more adversarial. They can play with different character dynamics and create new plot twists that deviate from the positive or neutral portrayals in the original show.
Maybe it's because she's often seen as the most talented singer in the show. Writers of fanfiction might just go with that perception and give her all the solos.