Well, 'hypothyroidism' was a very difficult and polymorphic badger in its day.

Isn't it still "its day"?

Think of it this way. There is a set of people with some clinical symptoms which look maybe-possibly like hypothyroidism. There is a another set of people with abnormal TSH. These sets partially intersect and form three subsets. Subset one is the intersection: people with both clinical symptoms and abnormal TSH. They are a clear case and there are no problems here. Subset two is abnormal TSH and absence of clinical symptoms. We interpret that as thyroid gland falling apart and expect clinical symptoms to appear in the near future. We are not concerned with people either.

Subset three is the one you are interested in: people with normal TSH and clinical symptoms. What about them? Well, as you mention diagnosing hypothyroidism solely on the basis of clinical symptoms is difficult. So in this subset some but not all people will have a thyroid malfunction, and some will have other problems, maybe instead or maybe in addition to thyroid issues.

By the way, the people who you insist on calling "fat, tired, and with dry skin" are in subset three. They exhibit clinical symptoms of hypothyroidism.

Your suggestion is that we give some dessicated thyroid to subset three and see if it helps. Well, it's pretty clear that it will help some people and will not help other people (for example, those fat and tired ones). However that is true of many medical interventions.

For example, there are probably males in subset three with low testosterone. So giving testosterone to subset three males will also help some people and not help others. There also probably people with low-grade systemic infections in there. Giving broad-spectrum antibiotics to subset three might well help some people and not help others. There are likely people with autoimmune disorders there...

Basically, if you have little idea about what's wrong, trying a variety of drugs hoping for a lucky hit is not necessarily a horrible strategy (depends on the side-effects of the drugs and the consequences of doing nothing), but it's not much advancement from the good old times.

Let me quote from West Hunter:

Back in the good old days, Charles II, age 53, had a fit one Sunday evening, while fondling two of his mistresses.

Monday they bled him (cupping and scarifying) of eight ounces of blood. Followed by an antimony emetic, vitriol in peony water, purgative pills, and a clyster. Followed by another clyster after two hours. Then syrup of blackthorn, more antimony, and rock salt. Next, more laxatives, white hellebore root up the nostrils. Powdered cowslip flowers. More purgatives. Then Spanish Fly. They shaved his head and stuck blistering plasters all over it, plastered the soles of his feet with tar and pigeon-dung, then said good-night.

Tuesday. ten more ounces of blood, a gargle of elm in syrup of mallow, and a julep of black cherry, peony, crushed pearls, and white sugar candy.

Wednesday. Things looked good:: only senna pods infused in spring water, along with white wine and nutmeg.

Thursday. More fits. They gave him a spirituous draft made from the skull of a man who had died a violent death. Peruvian bark, repeatedly, interspersed with more human skull. Didn’t work.

Friday. The king was worse. He tells them not to let poor Nelly starve. They try the Oriental Bezoar Stone, and more bleeding. Dies at noon.