Someone mentioned generating millions of (very short) stories with an LLM a few weeks ago: https://news.ycombinator.com/item?id=42577644

They linked to an interactive explorer that nicely shows the diversity of the dataset, and the HF repo links to the GitHub repo that has the code that generated the stories: https://github.com/lennart-finke/simple_stories_generate

So, it seems there are ways to get varied stories.