Are you asking if normal guys should be castrated so they can get accurate thyroid labs? -NOT
Both T and thyroid levels need to be normalized as otherwise each can pull the other down.
Without iodine replenishment, you would see what the problem was. But your body temperature tells that story. Some will fix an iodine deficiency and if temperatures normalize and they feel better that is the end of the story. We know that fT4 is low and TSH up, so you need to decide what to do.
In my own iodine deficiency, I was not interested in what any thyroid labs were as I wanted to get my iodine status fixed and then whatever the labs might have been was not material, not very scientific, but my attitude.