Story gives the context on girls events, it tells who they are, and why there is intercourse, how and where it happened, it let the reader to like characters, so there is a meaning and happiness. Without it, there is just another animation, moving blobs of colours.
I admit, i play a lot of those games, and sometimes writing is bad or walls of text, so i skip, but at least i try to know characters. Tho, GodWhim is not bad, not to much text, etc.
Great example here, Ryoko and Charlotte, without story those wud be just some horned girl and red cat, but after reading the story, player can have some bond with them, and feels better when taking care of them.