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Ah, I see. It was your mention of "long term" that sparked my interest, as there is very little long-term information out there on low carb diets, aside from case studies and whatnot. The studies you posted covered time frames of 7-18 days, in one they dropped carbs to 2% of caloric intake, in the other they adjusted the macros within the context of an 800 kcal/day diet. They both noted a decrease in T3. This is not particularly surprising. Switching over from any kind of carb usage to very low carb, or to a significantly calorie restricted diet, is going to cause some very predictable results. In either case, you're reducing the available energy sources, either directly through caloric restriction, or indirectly because the individual's body isn't able to take advantage of fat as a fuel right away.From my back pocket:
EFFECT OF CALORIC RESTRICTION AND DIETARY COMPOSITION ON SERUM T 3 AND REVERSE T 3 IN MAN
Isocaloric carbohydrate deprivation induces protein catabolism despite a low T3-syndrome in healthy men. - PubMed - NCBI
Low carb also lowers testosterone and elevates cortisol. I don't have references at hand and busy right now, but they are not hard to find.
Short term, someone going from a "normal diet" to keto is absolutely going to see a drop in T3, testosterone, probably serotonin (I haven't looked at that but it makes sense), and an increase in cortisol. This is known as the "adaptation phase," and can last anywhere from a week to a few months, and can either be "toughed out" or mitigated through a variety of practices. As @Ken Korcak mentioned, it takes a while to get things up and running when you turn the body's metabolism on it's head. However, I don't think we can look at adaptation physiology and assume it's representative of long term effects.
There is a special rabbit hole with regard to testosterone, but at the end of the day testosterone function ends up doing the same thing as everything else.