Um. If your "fundamental law" has all these exceptions, that's a good hint that maybe it isn't as fundamental as you thought. The law of gravity doesn't have exceptions. And no, it's not always better to "have the law". Sometimes it is, for practical reasons, and sometimes it's better to devise a better law that doesn't give you so many false positives.

You're missing the point too. Even gravity has exceptions - yes, really, this is a standard topic in philosophy of science because the Laws Of Gravity are so clear, yet in practice they are riddled with exceptions and errors. We have errors so large that Newtonians were forced to postulate entire planets to explain them (not all of which turned out as well as Uranus, Neptune, and Pluto), we have errors which took centuries to be winkled out, and of course errors like Mercury which ultimately could be explained only by an entirely new theory.

And we're talking about real-world statistics: has there ever been a sociology, economics, or biological allometry paper where every single data point was predicted perfectly without any error whatsoever? (If you think this, then perhaps you should consult Tukey and Cohen on how 'the null hypothesis is always false'.)

If we ignore all of that, we get superlinear scaling; but my guess is that if we include it, we would get sublinear scaling as usual -- in terms of overall economic output per single human.

Absolutely; if you measure in certain ways, diminishing returns has clearly set in for humanity. And yet, compared to hunter-gatherers, we might as well be a Singularity.

What does this tell you about the relevance of diminishing returns to Singularity discussions? (Chalmers's Singularity paper deals with this very question, IIRC, if you are interested in a pre-existing discussion.)