The best thyroid doctors out there note that a comprehensive physical looking for signs of hypothyroidism and a trial of thyroid hormone are the best ways to rule out hypothyroidism. TSH is an unreliable measure; for example, it decreases with age, leading to a reduction in T4 and T3, giving the false impression that because TSH is within range that things are fine. Stress also can lower TSH. There's always the possibility for thyroid hormone resistance. The late Dr John C Lowe had this, and said he was on a dose of T3 that was high enough to cause an endocrinologist to have a heart attack, yet this was the only thing that gave him relief from his intense depression and related symptoms.
Cortisol is needed to get thyroid into cells, but chronic stress, and high cortisol that can go with it, increases reverse T3 levels, which limits the conversion of T4 to T3. I'm skeptical of the claims, such as by Kent Holtorf, that rT3 inhibits the T3 cells, rendering them inactive to some degree, but I don't know how to explain why some people who try T4 feel worse; you'd think that if you increased T4, then no matter how much got converted to rT3, you'd still have at least some that led to increased (free) T3.
Then you have other interactions. A study I've recently come across notes the sharp increase in 2-hydroxyestrone with thyroid hormone. Even though this is the healthiest and anticarciongenic of the metabolites of estradiol, you still need the other two main pathways, 4- and 16-hydroxyestrone; the body has these pathways for a reason (it's through 16-OHE that you create estriol, I think). But what if you have low estrogen in the first place, such as people who are menopausal? Then you already have low levels of estradiol and 2-, 4-, and 16-OHE. Adding thyroid hormone to it, even when it's needed judging by testing, means you're draining estrogen metabolites that are already low away from 4- and 16-OHE even more.
I remember taking DIM (diindolylmethane), which had worked in balancing my estrogen metabolism, but when I took it with higher doses of T4 or NDT or T3 caused me to feel worse in a way that wasn't attributable to hyperthyroidism (more fatigue, brain fog, etc.). Perhaps what was happening there was too much 2-OHE and not enough of the other estrogen/estradiol metabolites.