If were testing high level results in multiple cases thats cool. But a lot of the time youre going to try different approaches that may modify or involve changing your output.
Which means the system design must be obvious enough that you have well defined lowly coupled units in the first place.
This is fine, if your already have a fair idea of how to architect your problem. But if you don't, it makes it harder to refactor your interfaces (in the same way that clients depending on your interfaces does). Of course, you can rewrite the tests, since you have control over them; it's just harder. And you don't have the TDD raison d'etre reassurance of working tests for this refactoring, of interfaces. Higher level function tests, yes; unit tests, no.