The main reason why desiccated pig thyroid (DPT) has been disliked by the medical community is complicated. It starts with one complaint that is true - there were large variability issues in DPT products even as late as the 1970s.
When levothyroxine came onto the scene it promised three things: consistency, uniformity, and safety. No longer would patients have to deal with potentially dangerous levels of T3 in treating hypothyroidism. No longer would individuals become hyperthyroid due to supraphysiologic amounts of T3 from DPT. That it continued to have its own consistency, uniformity, and reliability issues didn't really bother many doctors. It finally managed to live up to its promise when the FDA put its foot down in the late '00s and mandated much tighter controls.
But during that time, DPT also got its act together, and has much tighter manufacturing standards. The stability and uniformity is much better than it had been before.
The TSH test is actually very accurate. Third generation TSH assays are able to detect 0.02 mIU/L or less.
The problem is the way TSH testing levels are used without regard for the actual thyroid hormone levels. The relationship between TSH, T4, and T3 is much more complicated than it seems.
A good explanation of the latest research into it is here: https://www.researchgate.net/publication/263321383. The title of the paper is "Homeostatic equilibria between free thyroid hormones and pituitary thyrotropin are modulated by various influences including age, body mass index and treatment."
The reason why Barnes' paper showing that desiccated thyroid lowering cholesterol levels and seeming to prevent cardiovascular disease isn't cited is because he was basically making his patients hyperthyroid. Lower cholesterol levels occur in hyperthyroidism.
There is a doctor I know of in California who gives his patients supra-physiological levels of T3 hormone (cytomel) to increase their metabolism, to help them lose weight, and to lower their cholesterol levels. It basically suppresses the thyroid's own production of hormone. In the short term, it works. It's brilliant. But it's crazy. We have no idea what the long-term consequences are. And since I'm pretty sure he's not running a study on it, we won't.