Eh, "good" sea salt does contain iodine- fleur de sel, sel gris, himalayan pink. Not the commercial 'sea salt' (evaporated seawater). The questionable part, even with engineered hyper-iodized salt, is how much of the iodine is absorbed by the body. You're better off with seafood, dairy and eggs as a primary source, since the iodine is more bioavailable (potassium iodide or iodotyrosine vs. sodium iodide). Kind of like iron- you get most of it from meat, contradicting what your mama told you about spinach (bioavailable FE2+ vs. stable FE3).

The health benefit from sea salt is because it's not pure sodium chloride- the salty flavor comes from sodium, calcium and magnesium chlorides and sulfates, reducing the overall sodium intake and limiting the sodium imbalance in western diets.