I agree with you on a couple of points, disagree on others. TSH alone is insufficient for any sort of diagnosis of thyroid function. But taken together with free T3 and free T4 one can have a pretty good understanding of what is going on, especially when taken together with basal body temperature readings (.. the Dr. Barnes stuff). Then beyond that are the anti-thyroid hormone tests which can indicate Hashimoto's. In my opinion, all these tests when viewed together offer important insight as to whether one's body is producing enough thyroid hormones, or thyroid hormones are being utilized appropriately, or possibly one's pituitary gland is malfunctioning, or one's immune system is attacking the thyroid.
Unfortunately I don't believe any of these tests provide conclusive evidence on whether the thyroid has enough nutrients (iodine, selenium, ..) to do its job ... unless a goiter is present. Hence the recommendation on this forum to supplement based on the premise most folks are deficient in key thyroid nutrients, especially iodine.
However I don't want folks to believe these tests are the final word on hypothyroidism. Ultimately it is how a patient feels and the presence/absence of symptoms that should be the #1 factor in making a diagnosis. ... in my opinion.