I think there is quite a long tradition of books that say we should be dosing iodine. I think it originates from Wilkens who influenced authors like Fossa and Nilsen, and Delbeek and Sprung which give similar formulas for regular dosage of iodide.
In one of our systems iodine had dropped to 34 ppb by August last year, so I increased dosage to about the double. With doubling the dosage also the concentration in tanks increased to about the double concentration between ca. 50 and 100 ppb in different systems.
A difference could be seen soon in zooxanthellate gorgonians. A larger one, I think Pseudoplexaura, which had stopped growth resumed growth and showed a constriction where growth had stopped for some time.
A Briareum asbestinum which had started to show tissue necrosis grew new and larger polyps. Also other octocorallia (soft corals, leather corals and gorgonians) showed larger polyps.
Also scleractinians like Acropora spp. showed improved polyp extension, growth and colors but less pronounced. I think, like gorgonians and maybe other octocorallia, they incorporate iodine mainly in the organic matrix of their skeletons.
Besides the interesting article of Randy one of the more interesting articles I found in a quick search right now was
this one from Goldberg et al. on corals and coral rocks in the diet of a parrotfish. In this research iodine increased by a factor of 38 from live coral (3.7 ppm on average) to coral rock (142 ppm on average). In coral rock the concentration of iodine found was by a factor of ca. 2366 higher than in the seawater (ca. 60 ppb) surrounding the rocks. For comparison: The enrichment factor for calcium is ca. 878 and 756 respectively, from ca. 410 ppm in seawater to ca. 36 % in live coral and 31 % in coral rock. Similar processes may influence iodine consumption in reef tanks too.