One way find out if psychotherapy is actually helpful, is to use scientific and statistical methods to research the outcomes. And then it wouldn't be guesswork.
The research databases are out there, and are free. Take a look!
The problem here is that the illness often affects the patients ability to actively participate. In order to 'be truly committed to achieving health' the patient already needs to be greatly improved from the illness which is causing them the problems, since the lack of motivation to do so is usually part of the problem (if we are talking about depression, which to some degree often accompanies SA).
Its like inventing a physical therapy for someone with weak legs, and saying its the patients fault for not having the strength of legs to do the therapy to strengthen them.
This example works against what you're saying. Physical therapy is designed to include individualized work based on the client's needs, desires, and goals, and then gradually increasing abilities within his/her potential. Psychotherapy is really not that different. It does take a different approach, since assessing interaction styles and beliefs and so on, is not so tangibly obvious from the get-go. But it is not fundamentally different.
If we pretend that motivation and energy, and commitment are completely separate from the physicality of the brain, then we can blame the patient for a lack of compliance / motivation.
If you believe that you cannot make choices and that nothing can get better, and that you have no control over your life, you may decide that psychotherapy can do nothing for you. Why bother?
That kind of belief is self-fulfilling (I can't do anything so I won't. See? - I'm not capable of anything. That belief is true.).
If we are realistic however, we have to accept that the way the patient behaves is to a significant degree impacted by the mental health problems, because mental health problems affect the brain, and the brain affects how the person behaves and thinks.
And vice versa. Behavior and thoughts influence feelings. This is so well-established in research literature as to be canonical. Your brain has extensive feedback loops from frontal lobes, thalamus, and limbic regions. Interpretations and thoughts from higher areas have a top-down effect.
It's not so much, does A --> B or does B --> A. A and B affect each other in a continuous relationship. This is not to say that psychotherapy has limitless potential to change and improve every person to some kind of arbitrary standard of normalcy but then again, no treatment can do that.