I've always wondered why she never uses it. It's not even just in the anime, she carries it around with her in the visual novel too. Maybe it would just be too convenient, or it could even be just for show, IDK
Maybe they intended for her to use it at some point early on in the development but forgot about it, or they could have decided it would be more dramatic that she mutilate her victims using more brutal methods.
But think of the episode when Takano pulls out a hand gun and shoots her and all the other characters (with Rika being the exception), why wouldn't Shion use her gun in that situation?