"If we hand this out to fat, tired people with dry skin, does it work?". And the answer to that is: "On average they can't tell the difference between that and placebo.

I'm confused. Aren't these clinical symptoms of hypothyroidism?

Besides, "works / doesn't work" seems like a too crude approach. There is a large middle zone of "works for some people some of the time" and there you have roll up your sleeves and get into the messy details which might still not give you enough information to be able to predict for which people at which time your treatment will work (or not).

The "theoretically correct" approach would be, I think, to do a deep dive into biochemistry and figure out all the links in the mechanism connecting the T levels in the blood with the activity of the mitochondria. Once you do that, figuring out which link is broken in a particular patient subset shouldn't be too hard. But the initial research, mapping out the chain of effects, looks daunting.