"Exhaustively covering the search space" or "hitting specific edge cases" is the wrong way to think about property tests, in my experience. I find them most valuable as insanity checks, i.e. they can verify that basic invariants hold under conditions even I wouldn't think of testing manually. I'd check for empty strings, short strings, long strings, strings without spaces, strings with spaces, strings with weird characters, etc. But I might not think of testing with a string that's only spaces. The generator will.