That said, the biggest problem I've had is the "living code samples". I'm not sure of the exact name, but the feature where you display a component on the page and click the Show Code button to do a flip and see the code that drives it. The libraries we use that use Storybook are fairly complex, so I'm not sure how much that has something to do with it, but not a single "living code sample" has been a self-contained example.
When I look at code samples for libraries, I expect I should be able to more or less copy/paste the code directly into my application and it should just work (once the dependencies are added). This includes things like import statements as well so I know where things are being imported from in the case of multiple import paths for a library. Unfortunately, instead it's been lots of wrappers and helper functions in the storybook examples and I've only gotten vague answers of "storybook limitations" as to why they're not totally self-contained copy-and-paste-able.
I'll see if I can speak with one of the engineers at work to ask more about the limitations he meant when I complained about the examples not being self-contained and get back to you on that.
I hope this makes sense and is actually helpful!
But just using straight up Storybook as documentation, I agree that isn't very good. Whenever I'm just given a random Storybook, my success with that library has been pretty low.
I don't know if this is a doc writing problem or a product problem with how Storybook works (is it even supposed to be a documentation product? I don't know), but so far my experience has been a 0 for 2 with Storybook-based documentation being significantly worse than normal.