Why is a story not called a “-logue”, though it has a prologue and an epilogue?

Prologue and epilogue use a form of the Greek λόγος (logos), which means “a speaking”. The word lecture is the word for the speech itself, stemming again from λόγος. Though it doesn't use -logue, it maintains the same roots.

Note that lecture has the alternate meaning of “a reading”, so it makes sense as a story. Lecture has lost this meaning in most cases, but even using the meaning speech fits in with prologue (before speech) and epilogue (after speech). Since pro- and epilogue refer to a “speech”, lecture fits in even with its current usage.

If I just wanted a more formal/technical (to literary discussion) term for “story”, I’d probably go with narrative, or simply work, if I wanted to avoid bringing up discussion about whether the story is in fact a narrated thing. I would likely avoid lecture, since its most salient meaning in modern English is “reading/explaining something out loud to other people” (“my mom lectured me about my grades”, “the teacher lectured about chinese history”).

As for why there’s no word for “story” analogous to prologue/epilogue, all I can say is that English happens not to have a word of that sort. There are a myriad of ways that a language can derive a word for a concept, and English happens not to have derived a word from Greek -logue to refer to the story itself as opposed to the epilogue and prologue, like it did for prologue and epilogue themselves. Instead it uses a French borrowing story, or a Latinate borrowing narrative. You might as well ask why English doesn’t have a French loan for “invention” but instead has a Latinate one.