I think it will help most if I explain the incentives for scientists (at least in the US). From their first day in the lab scientists are rewarded most for generating data and making discoveries. The more novel and paradigm shifting the discovery the better - as it opens the door to high-impact publications and future research money. But "extraordinary claims require extraordinary evidence" and the more unexpected the finding the more difficult it is to convince your peers and get it published.
Somewhat idealistically, this has two consequences for a good lead scientist:
1) hew will guide his lab to explore the unexplored
2) and subject the most novel and promising findings to the most stringent experimental verification.
So the answer to your direct question - yes probably someone somewhere tried to test the iodine-breast cancer hypothesis, but since it is not a major topic in breast cancer research the experiments have probably failed and were not published and thus independently replicated
I think it will help most if I explain the incentives for scientists (at least in the US). From their first day in the lab scientists are rewarded most for generating data and making discoveries. The more novel and paradigm shifting the discovery the better - as it opens the door to high-impact publications and future research money. But "extraordinary claims require extraordinary evidence" and the more unexpected the finding the more difficult it is to convince your peers and get it published.
Somewhat idealistically, this has two consequences for a good lead scientist: 1) hew will guide his lab to explore the unexplored 2) and subject the most novel and promising findings to the most stringent experimental verification.
So the answer to your direct question - yes probably someone somewhere tried to test the iodine-breast cancer hypothesis, but since it is not a major topic in breast cancer research the experiments have probably failed and were not published and thus independently replicated