Re: a recurring theme ... was that the three laws didn't really work all that well
The stories focus on the rare instances when things go wrong, and are seen as abnormalities against millions of robots not causing any fuss.
Irrelevant to the force of Asimov's robot stories. The point isn't to explore whether the Three Rules produce an acceptable defect rate or are probabilistically "good". It's to consider a series of logic puzzles in which a system of three simple axioms is shown to produce surprising results.
In that sense the Three Laws work "poorly", for their ostensible purpose (though well for their pedagogical one), because they appear to offer simple, absolute guarantees, but it's possible to find numerous exceptions. The principle of least surprise is violated.
It's certainly possible to claim that in the world of the robot stories the Three Laws work "well" in a practical sense. That's much like Chaitin's argument that Hilbert's Entscheidungsproblem was a resounding success, because Church's and Turing's proofs that it can't be solved introduced formalisms that were invaluable in spurring the development of digital computing; a mathematical "failure" (not really a failure, of course, and Chaitin doesn't characterize it as such) contributed to a major technological advance. You could say the same of the Three Laws (in their world): mapping their logical "failures" helps cement their application in technology.
But reading that as a principal theme of the stories rather goes against the interpretations most readily inferred from the text, I think. The stories are about how the Laws fail.