Melatonin production is influenced at least also by: Zinc, iron, calcium, copper, P5P (active B6), and tryptophan. Selenium, iodine, and manganese are involved in indirect ways. Many people are deficient in most, or all of those.

To be fair, some of these, like iodine and selenium, have always been problematic in some regions, like Switzerland (lots of goiters). But I find it less than ideal that only some minerals are fortified in bread and milk etc, because their deficiency is very obvious. While all the other minerals are not fortified because their deficiencies are less obvious or less well understood.

A healthy human body contains quite a few minerals in greater abundance than iodine: copper, bromine, strontium, rubidium, gallium, silicon, zinc, iron, and the electrolytes. Some of them don’t even have lab tests (not that blood tests work well for minerals, which is another issue - blood is short term transport for most minerals, not storage).