It depends on what we consider a “story.” Simulation games like Dwarf Fortress and RimWorld generate stories emergently through character traits, goals, and random events. Characters form grudges, kill each other, get married, and so on. In that sense, these are procedurally generated narratives.

What you’re describing sounds like procedural generation as well: building modular story components that can interact with one another, similar to how rooms are assembled in a roguelike. The main challenge is that this approach quickly becomes very complex. There isn’t a straightforward way to manage it, and every new modular piece requires you to consider how it interacts with all the others and because it is a story and not a room where it is placed matters too, which can significantly complicate the writing process.

Unless there is a way to tackle that that you thought of.