Having experienced burnout and resulting chronic fatigue syndrome (which is really just an extreme version of burnout that persists long after the stress has ended), I pretty much agree with everything you say. However it's incorrect to say that burnout is physical rather than psychological as psychological factors do play a large part in determining whether or not you experience burnout.
Yes, CFS has a psychological component… In the way that, if X happens the same to you and me, and you don't care, but I do, then my adrenals/thyroid go into overdrive, yours don't; I get sick, you don't. Some people get CFS because of minor stress, some people don't get it until their life is a living hell. That's the psychological aspect of it.
But that doesn't make it a psychological disorder in any way, shape or form. Mind and body are just simply not separate. I have been depressed in my life. I was not depressed before my illness or even during it, except the natural kind of mourning a person goes through when suddenly they can't even stand up.
I'm sure lots of people have concomitant depression, since so many people are depressed, period. But many also do not. (I'm one of them.)
I'm more interested in understanding what is going on in the brain/body rather than arguing over terminology. Both psychological and other factors seem to cause burnout/CFS, although psychological factors do seem to be the most important. Depression is a resulting symptom, not a cause.
Stress and burnout affect different people in different ways: some people get depressed, others develop chronic pain (fibromyalgia, ME), others have chronic fatigue etc.
As for the psychological factors that seem to be important: motivation, goals and emotions all seem to play a large part.
While you're correct that CFS is not entirely psychological (functional would be a better term), it does appear to be mostly caused by psychological factors. If you look at the main triggers for CFS they are: job stress, relationship stress, and viral infection - and there is some doubt as to whether the viral infection is a cause or just a symptom of a weakened immune system.
If I am depressed and jump in front of a train, or if I think that's a safe and normal thing to lie on the tracks, or if somebody pushes me, or if I trip, the result is the same: Splat.
There's little point in saying "Splats are primarily psychological" if accidents and mistaken facts seem to be at play often enough. Or if people splat other ways (e.g. in car crashes, tightrope accidents). The result is the same. Splatty splat splat. The outcome only tells you so much.
I can tell you one thing: Totally overhauling my "motivation, goals, and emotions" did absolutely diddlysquat in making me better because while I started off with a combination of routine infection and "psychological" stress (which, of course, is a kind of misnomer because you can measure it with blood tests)... it did permanent damage to my mechanicals. Splat.
Also, a lot of doctors think FM/ME/CFS are the same thing. And a lot think adrenal fatigue/hypothyroid and CFS are the same thing. Maybe they are separate but cause each other.
Genetics certainly play a part; hypothyroid is incredibly heritable, for example. It causes lots of the same symptoms and may be a symptom/cause (or both) itself.
But nobody claims that hypothyroidism is psychological, not even slightly, much less primarily.
But the cause for an individual almost doesn't matter. You have to cut stress no matter whether it was a primary cause for you or not.
