One other things to think about, When many were following Atkins and they lost weight, their LDL went down too. The thyroid controls the level of LDL. I am not saying that everyone on Thyroid can get off, but maybe people like me who are on a small dose can do somethings to correct it before it get's too bad off. Sort of like pre diabetes, when people use food to control their blood sugar. For me, it is worth a try- I will do it under a doctors care, and if I do this, I will eat lean meats, lots of vegs and good fats, and fruits.. limited milk ( calcium) and no grains. Then I will get my labs done again. Then post back here with my outcome... again, I am not saying for others to follow, I am in the early stages so it MIGHT work.
I'm not sure if you're addressing someone specific when you typed "you have stated..."
You're correct that exercise can help keep your blood pressure in check, but you have the wrong idea about thyroid "converting energy"... it doesn't work that way. The thyroid produces hormones, T4 and T3... The hormones are what controls metabolism, heart rate, body temperature and other functions.
Of the Total T4 in your body, most is attached to a protein and is unusable, which is why we test the "Free" (unbound) T4. T4 isn't used directly by individual cells; it must be converted to T3, but like the T3, most of the T3 is bound by a protein, which, again is why we test the Free (unbound) T3, because it's the Free T3 that's used by the individual cells in your body.
Protein helps your body build muscle; it has little to nothing to do with thyroid. When we talk about protein binding to the T3 and T4, we're referring to protein molecules in your blood that transport the T3 and T4 throughout the body. It doesn't convert anything, it transports.
Fiber doesn't convert anything either... Too much fiber, too close to taking your thyroid medication can block absorption of thyroid medication. Gluten is not the same thing as fiber. The answer is "no"... if you need thyroid medication, going off fiber and eating only lean protein would allow you to get off the thyroid med, besides it wouldn't be healthy, because your body "needs" fiber in order to help digestion and other functions.
You can't believe "everything" you read and it doesn't always apply, literally.
Nobody can tell you what to do, but if you get off your medication and try to control your thyroid with diet, alone, you will be disappointed and could very easily end up quite sick... Hashimoto's and hypothyroidism are not like pre-diabetes... I have pre-diabetes and I've turned it around with my diet; I've also brought my cholesterol levels back to normal with exercise and diet, however, Hashimoto's and hypothyroidism can't be controlled like that and I would never dream of going off my thyroid medications.