The causality actually goes the other way. The Morton Salt Company revolutionized salt by adding minute amounts of clay to prevent caking, which is one of the advantages that allowed them to achieve a near monopoly in salt production at the time iodine deficiency became understood. That meant that iodizing Morton's salt was basically iodizing all the salt.

However, the iodine is independent of the anti-caking additives. You can have iodized salt which still cakes up when it is humid, but why would you want to?