I know that you specified "with respect to the thyroid", but the most obvious example that I can think of for the consumption of brassicas is that they show anti-cancer properties. And DIM is derived from brassicas, it normalizes estrogen metabolism(so, I suspect, although I have not researched this, that the cancers that brassicas effect, are probably hormonally driven).
I took DIM for quite some time. Fleshas, for one, recommends this for FBD patients.
Maybe the estrogen-normalizing properties of brassicas are why I crave them so much, and I always have! :)