"A perfect implementation of the wrong specification is worthless."
The point of BDD is exactly this: bring specification to the scene, give it a first class citizen status, it becomes a live entity in the system, more influential than before. I don't believe Readme or any other document can be as influential as a Cucumber feature, for instance.
your idea works for libraries that are small, it's appalling for libraries of any significant size.
the point of a readme is to provide a useful summary that is quick to start using for the critical path use cases.
if you look at a web framework in a language you don't know as an example, and try to find the introductory use cases in the tests, this should give you some idea of what you're suggesting.
Really could you see a developer reading the entire .net or java standard library test suite before using either Java or C#