If somebody hands over an application to me where configs have unit tests, this means to me that the application can fail catastrophically under certain (unwanted) configurations. And seeing how I might be the owner of said applications, chances are high that at some point I would need to change the configs.

I, personally, would rather prefer straightforward static configuration and very well written documentation on why certain configurations make more sense than others. That way, I know how and when to change something in the configs.

I absolutely do not share the view that "tests are documentation", because they do not communicate the most important thing in software engineering - the intent and reasoning behind a certain design.