Well seen, for the impact of deiodination.
When halogens take the place of iodine on thyroid receptors, it's hard to get the right amount of active hormones (T3).
And the problem is all the more serious / harmful for women: fight between thyroid and breasts to capture circulating iodine. iodal would be then required; not just the RDA (150 mcg; much higher).
A protocol must be followed.
Halogens: Fl > Cl > Br> I. (stronger force of attraction for bromine).
In iodine-sufficient areas, the adult thyroid traps about 60 μg of iodine/day, either from dietary iodine or from iodine released during thyroid hormone therapy.
But much higher for iodine when there is inflammation or an immune reaction (mastocytose).
Additional info
Why does bromine displace iodine?
The bromine displaces the iodine from sodium iodide as it is further up in group 7 and therefore more reactive than iodine. Iodine is lower down in group 7 and therefore less reactive than chlorine and bromine.
Electronegative elements have the property to remove electrons form the elements to which, it is attached.
Fluorine is an extremely powerful oxidizing agent.
The oxidizing power of the halogens varies in the order: F2 > Cl2 > Br2 > I2
The order of reactivity is chlorine > bromine > iodine. This is because chlorine could displace bromine and iodine, bromine could only displace iodine, but iodine could not displace chlorine or bromine.
Explaining the trend:
When an element in group 7 takes part in a reaction, its atom's outer shells gain an electron and form negatively charged ions, called anions. The less easily these anions form, the less reactive the halogen.
When the atoms become larger, the outer shell becomes further from the nucleus. The force of attraction between the nucleus and the outer shell decreases. An outer electron is gained less easily. The halogen becomes less reactive.
Source: BBC - Halogen displacement reactions https://www.bbc.co.uk/bitesize/guides/zg337p3/revision/3#:~:text=The order of reactivity is,not displace chlorine or bromine.