Iodine is an essential element needed for proper thyroid function. In some thyroid disease cases however, iodine supplementation may be contraindicated (risks involved).
Many companies that manufacture supplements advertised to boost thyroid function often place high levels of iodine content in them or include ingredients that are rich in iodine, such as kelp (seaweed-algae). While reasonable levels of iodine intake is healthy for people with non-diseased thyroid glands, it can have adverse effects in some cases ...

Hashimoto's is an autoimmune type of thyroiditis that leads to hypothyroidism. While there is no cure for the disease, the resulting hypothyroidism can be treated.
Hashimoto’s thyroiditis affects approximately 14-million Americans and is 7 times more common in women than in men. It is the leading cause of hypothyroidism in industrialized countries ...

It is my opinion, and one I know also agrees with that of most medical professionals, that trying to replace thyroid hormone medication, containing actual thyroid hormone, with a supplement containing no thyroid hormone, or an inconsistent amount, could actually be dangerous.