WHy is radioactive iodine useful in diagnosing and treating certain thyroid conditions?

Very simple reason: The thyroid is the ONLY organ in the body that stores, aculates and excretes Iodine. Thyroid hormone contains iodine and is essential for normal life. By using radioactive iodine, we can force the thyroid to uptake it and, if the dose is high enough we can use it to "kill off" the gland if it is overactive. Once it is "dead" then we replace it with synthetic thyroid hormone in normal, controllable doses.