He knows that ultimately a tool is neither good nor evil, but depends upon the wielder. And as per his version of Game Theory, Rand is right where Moridin wants him.

Think about the progression we've seen with the CK.
- Rand uses it to Cleanse Saidin.
- Rand uses it to destroy Graendal's lair, at the cost of burning souls of people out of the pattern (preventing their reincarnation for some time at least). Still, it's worth it to him since Graendal would have killed more.
- Rand uses it as a balance to the TP, finally acknowledging the true extent of his power addiction.
- Rand goes ballistic after meeting Hurin and nearly destroys the Borderlander army because he suspects they might be traitors (IMO, an unspoken thought of his was that Demandred was behind that army). He justifies this by stating that it would just be a warning, that they were doing the DO's work, and that he would not hit Far Madding, only the army camps.
- Finally, Rand nearly wipes out the Seanchan army, for similar reasons to the above.

In hindsight from "Veins of Gold", it might seem like Rand was acting on his own, or merely at random, but I'm fairly certain that his situation has been deftly engineered by Moridin.

Imagine the scenario where Moridin takes the CK. As I've said before, I think that Moridin is burnt out and cannot wield it himself. So who would he give it to? Any of the other FS or Dark Asha'man can't be trusted with that much power. He has two options:
1) Keep it for himself (essentially destroying it, removing it from the game), or
2) Let Rand, who is so easy to manipulate and manoeuvre, keep it. I think that Moridin understood the Cleansing well enough to realise that it was Shadar Logoth, not the CK, which destroyed the Taint. While Moridin was willing to let Rand die to prevent the Cleansing, he knows it was a one-off event. The real threat there was Shadar Logoth (which may hint at why the Shadow wants Fain so badly). Now, he knows that Rand is beginning to think like him. So why not give him the power to unleash his anger and cause massive collateral damage? As Moridin must surely realise, Rand's greatest anger is directed not at the DO but at those who fail to see the threat the DO poses - notably, the Borderlanders and Seanchan.