The better explanation is the logical one - it was overlooked or impossible to steal it at the time. We don't even know if SH looked into the box. More likely he sent Elza and she fetched the band. The thought of straying from her mission would incomprehensible when serving a walking terror like SH.



I don't think it was overlooked, because they obviously had the intel of where the male a'dam was. SH and Moridin realized that if Semirhage brought Rand to Shayol Ghul then it was 'Game Over.' The CK wouldn't work at Shayol Ghul, and they would likely have turned Rand to the shadow before a proper rescue effort could have been mounted. Therefore the CK was no longer needed.

Therefore they left the CK behind because it served them better to leave it behind if Semirhage failed to take Rand to Shayol Ghul. They didn't overlook the CK or accidentally leave it behind-- this was a quick-strike operation and they knew exactly where the male a'dam would be. If they knew where the male a'dam was, then it follows they knew the Ck would be there too. They didn't overlook it, they just realized it wasn't needed anymore if Semirhage suceeded. More perplexing, however, is where did they get this intel?

We can argue all we want about the rest of my theory, but it only stands to reason that the pattern had no use left for the CK and therefore it allowed it to be destroyed. Therefore there is no point in arguing about what the light should and could have done with the CK.