Was doing a bit of reading on glucagon and came across some info that high levels of glucagon cause T3 levels to drop and RT3 levels to rise. And it does this by affecting the liver and preventing the conversion of T4 to the active hormone T3 (not by affecting secretion by the thyroid).
So I would imagine this would mean that if you don't have a functioning thyroid and you are on T4 (therefore rely fully on liver conversion for T3) dieting would cause low blood sugar which would cause high glucagon which would in turn cause hypothyroidism by reducing T3 levels. Thereby causing the metabolism to slow and less calories to be burned and no weight loss. Also causing other hypothyroid symptoms too I would imagine.
One argument for giving thyroid patients T3 as well as T4.