These issues are not easy, nobody really knows. I recently posted some writings from an MD under the topic of Manganese, that suggests if vitamin B1 is not "balanced" with manganese, it can impact thyrotoxicosis. This is just one potential other factor to consider, and there may be scores of other similar considerations.
Its probably true in the vast majority of cases that supplying an essential mineral like Iodine to a person who is deficient in it will have benefits, like supplying vitamin C to a person with scurvy has, etc.
And while it might be ok for some to take large amounts of iodine, obviously it can have detriments for others. For those others, this should not be looked at as being a bad thing, rather, the Iodine having a problem is an indicator that something is amiss somewhere else. For example, the manganese / vitamin B1 balance. It could be in some cases that all the person has to do is check their manganese and B1 levels.
Maybe the Iodine Problems forum can help to identify why a small fraction of people have trouble with iodine. I personally view such reports as indicating the person needs to look deeper, at other things than iodine itself. In that regard, Iodine is like a canary in a coal mine.
As with anything, moderation is a good idea. Even though some MD's recommend 25 mg of iodine per day, I restrict myself to about 6 mg once or twice a month.
I think there is a BIG PROBLEM with the Iodine Loading test some MD's and others promote - it assumes that all people will expel excess iodine once the body is saturated. But those MD's and others overlook the fact that there are other known reasons for the body not absorbing iodine, including Dr. Jorge Flechas himself when he states that estrogen blocks iodine absorption. Which estrogen ? estrone ? estradiol ? estriol ? It could well be that lack of hydroxylated steroids is what blocks iodine absorption and gives a mis-leading result in the Iodine Loading test, and ensuring adequate supply of the minerals necessary for steroid hydroxylation would be something to at least consider before giving credence to the loading test.
I think in general, if a person is "low" in iodine, there is a good chance that they are also low in other essential minerals and vitamins. It would be rare to find a person whose body is only solely deficient in iodine. I think deficiencies in the other minerals and vitamins are a big contributor to why people who have trouble taking iodine, have trouble taking iodine. Maybe the Iodine Problems forum can help expose some of these other issues in a way that a pattern emerges and we all learn something.