You fail to provide a good reason for why they left the CK behind yet you still call the idea stupid if true. You also forget that Rand, himself, realized how dangerous the CK was and voluntarily destroyed it himself. He realized that no mortal could properly wield that amount of power. The CK was the pattern's answer to the taint, but it was not needed for the Last Battle-- which is why the CK was not mentioned in the Karethon Cycle. Therefore you idea of the CK doing a lot of good for the light doesn't make any sense.

The CK in the hands of a madman like Rand was a near ideal situation for the Dark One. Rand very nearly did the Dark One's work for him by destroying the pattern. It may not have been the primary plan, but I think it is quite reasonable that the Dark One left the CK for Rand on purpose. I have yet to see a better explanation for why the CK was left behind.