Why it is done this way
TSH is a screen, not an evaluation
A patient can have a TSH squarely inside the range and still have a thyroid problem worth treating.
TSH is a pituitary hormone. It is a useful screen and a poor complete picture. Free T3, free T4, reverse T3 and thyroid antibodies are what show low active hormone, poor conversion, or Hashimoto's years before the screen moves.
None of it is exotic or expensive. It is simply not routinely ordered.