But they wouldn't be immune to deficiency, merely eating a diet that prevents the deficiency, through some sort of craving for seafood which is virtually impossible to discern from cultural. We do seem to have a preference for variety in food.

I'm not sure. It may be that iodine is the only way to do the things it does in mammals

My understanding is that it is used in signalling molecules used to control growth, but is not used in any key steps in main metabolism itself. Animals can survive on very little iodine, it seems - stunted and not growing right, but i'd imagine given enough time evolution would find a way to re-do that growth control using another molecules for hormones.