Yes; I'm a lot weaker in my statistical understanding, but it seems like it would be a fantastic way of slicing up the testing pie.

Unit tests are kind of handy if you've got some sort of "fencepost" style error where you need to figure out a piece of logic that was overlooked. But that's about it.

This sort of testing would way more relevant, because it's a way of focusing on "what (data) do we 'well' right now"?

I'm thinking that such sort of systems might be useful as a basis for performance or concurrency testing for example.