Do you really need iodine to be healthy?

Yes. Iodine is an essential ingredient for making thyroid hormone. Your body needs about 100 mg of iodine daily. Most Americans get much more than this, because most processed foods in the US include salt supplemented with iodine. It is also present in many commercial baked goods as a preservative/dough conditioner, in red & brown food dyes, and in seafood from the ocean.
Yes. Your body needs iodine to make thyroid hormones (among other things). Without it you would develop hypothyroidism and a goiter. Luckily, iodine deficiency is almost unheard of in developed countries due to salt being "iodinated", and we all get plenty of salt in our diets.