People with hypothyroidism do fine when taking medication containing their daily dose of thyroid hormone. This means that the signaling function of the thyroid hormones is, in principle, unnecessary. If a constant signal would do, then there is no need for that signal in the first place, as you could just by default switch on whatever process is now switched on by the thyroid hormone. So, what's the whole point of regulating metabolism via the thyroid hormone, especially considering that it predisposes us to thyroid disease?
The answer is in special situations, where a trade-off has to be done between thermogenesis and energy saving. This applies to hibernation of animals as well as to critical illness in humans.
This kind of adaptation is referred to as TACITUS syndrome (thyroid allostasis in critical illness, tumours, uraemia and starvation), NTIS (non-thyroidal illness syndrome) or ESS (euthyroid sick syndrome). In this situation, total and free T3 are downregulated, and, in special cases, TSH and T4, too. See an open review article by Wajner and Maja, which is available from http://dx.doi.org/10.3389/fendo.2012.00008 , for details.