A huge reason why Iodine fell out of favor is the "Wolff-Chaikoff Effect," which has been a disaster for public health.
An experiment was done that resulted in a case of hypothyroidism, which researchers misinterpreted as being caused by excessive Iodine intake. However, the individual was given intravenous radioactive iodine -- which is toxic. It had nothing to do with food or supplement iodine intake, and the two are completely different.
Yet, tales of this experiment quickly spread, creating a fear of iodine that caused it to be removed from the American food supply for the last three decades.