Okay, but my suggestion is that this mode of empirical verification just isn't good enough. People have been using this obvious method for decades, and we still can't solve face detection (face recognition is presumably much harder than mere detection). This implies we need a non-obvious method of empirical evaluation.

If we're talking about "empirical verification"/"empirical evaluation", then we're talking about how to check if a possible solution is correct, not about how to come up with possible solutions. This method of verification keeps coming up negative because we haven't solved face detection, not the other way around.

So if we're doing something wrong, it's in the way we're trying to formulate answers, not in the way we're trying to check them. And even there, saying we need more "non-obvious" thinking has the same problem as saying that something needs complexity: it's not an inherently desirable quality on its own, and it doesn't tell us anything new about how to do it (presumably people already tried the obvious answers, so all the current attempts will be non-obvious anyway... hence Riemannian manifolds). If you have some specific better method that happens to be non-obvious, then just say what it is.