Iodine concentrations in cow’s milk in Central and Northern Bohemia
Studies on the effects of rapeseed meal on thyroid st... [J Nutr. 1979] - PubMed - NCBI
So going/staying primal will probably reduce the wash-out from these sourches. But it won't reduce any unwanted halids you may have picked up from the environment we live in.
And I still believe that the average american (and european too) get too little iodine in the first place, so that the need for most people is unsatisfied.