Paula......The "reasons" people may or may not take iodine supplements, pretty much relate to my thoughts on these supplements. The average adult who consumes a healthy balanced diet is ahead of the game of course. Normally, using iodized table salt in cooking and very lightly in our foods, will suffice to supply our need for iodine.
Pregnant & nursing women must take an added supplement. Iodine is crucial for babies and children's brain development.
Aside from this, the reality is that our entire body needs iodine, in particular our thyroid. In addition, our body tissues use and absorb iodine for healthy, properly functioning skin, brain & bone marrow, to name just a few.
As for HOW MUCH? Each individual along with their Primary Care Physician needs to research and determine the appropriate, safe level.
While iodine is a beneficial need, too much can be harmful.
Other than pregnancies (decades ago)...I have never found it necessary to consume supplements other than using iodized salt.
I hope this information helps your curiosity. Peace, Paula