While I agree with most of what you say, the problem is that a lot of studies have been done on the HPA axis and cortisol in CFS/burnout, but there is no agreement. Some studies find low cortisol, others don't. There is definitely HPA axis dysfunction, but nobody can seem to pin it down. I suspect that if you measured cortisol throughout the day and correlated it to a symptom diary and/or a stress test, you might be able to come up with a diagnostic test.

The other issue is that there is no cheap and easy cortisol test like there is for blood glucose. As far as I can tell it would be possible to develop such a test, but nobody has done it yet for a number of reasons (lack of demand, cost, FDA approval, etc).

If someone were to [1] figure out a definitive test for burnout/CFS and [2] develop/patent a home testing kit they would be very rich and help a lot of people into the bargain.

As for Teitelbaum: while he does have some useful stuff to say, he also peddles a lot of quackery.