The most common kinds of hypothyroidism are due to the thyroid being damaged. Adding iodine can't help, but there are several known ways it can be harmful.
Iodine can still push forward the pathways that synthesize thyroid hormones and increase levels, even in many cases where the thyroid is damaged, e.g. hashimotos. In fact, most hormones can have their synthesis pushed by megadosing on their chemical precursors- however that can be unsafe of course.
Yes, it can be harmful, and depends on context- but you'll find a ton of info online about people successfully self treating hypothyroidism with high dose iodine.
Here is some more detail on the context, and mechanism for why people often react differently to this:
> On the other side, doctors such as X, Y, Z, have claimed success prescribing high doses of iodine for Hashimoto’s and for breast and thyroid cancers.
The blog post above didn't take long to go off the rails. Already in the introduction, the only "experts" in favor of high iodine are a bunch of quacks saying it can cure cancer. I have no sympathy for these fellows who are making a quick buck on the backs of vulnerable cancer patients.
You are thinking in terms of authority instead of as a scientist synthesizing diverse evidence and considering possible biological mechanisms.
They are not vouching for those cited three doctors here, but considering their claims as weak evidence within a broader context.
If you’re going to look just at authority, consider that the authors of that blog are well respected cancer researchers who recently discovered a promising new cancer treatment in active clinical trials. I’m an academic in a related field, have met them personally, and can vouch for the fact that they are innovative out of the box thinkers with a lot of good ideas.
It is important to distinguish between quackery and open minded scientific thinking. This is how the “sausage” of new medical discoveries are made: by creative people thinking “off the rails.”
Again, I am not in any way advocating for high dose iodine to anyone- and I would not do it myself. Only that it can increase thyroid hormone levels through a well understood mechanism, and some people have treated their hypothyroidism this way.