@littleblackship Reading and writing is no doubt connected, and as @turtely clearly states, fictional stories allow us momentary escape from our own mad reality, where things can be a little different, and in a way, it gives us as readers a lot of inspiration. This is probably why there is fanfiction, after reading a story, some people may feel inspired and want to create a story, and fanfiction, while still more or less based on the original works, still has a lot of imagination within.
Also, what you read changes the way you write. I've always found my writing style very similar to the style I have been reading in that time, everything from the character naming, personalities, to grammtical structure and vocabulary. For example, after reading the original Sherlock Holmes novels continuously, I found myself always trying to talk/write much more old-timey.