Basically, different types of games require different types of stories. Phoenix Wright games absolutely need stories to work. Adventure games are greatly enhanced by stories. RPG's revolve around the story, even if the gameplay never does. Rythm games never really need stories, but I imagine that made right it could be an interesting result.... and so on and so on.
It's not so much about if you want the stories or if you like them or not. It's more about what a story can bring to a game. Some games need them, some games don't.
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