I can't speak to how well it works for all of those issues, but one of the things wrong with it -- not with it, rather, but with the privileged place it's been given in the current medical model of mental health issues -- is that it's close to useless for people with a trauma history, and trauma is the underlying cause of all five issues I mentioned for many people. (I could write a separate post on why it's been given that privileged place, but I'll leave that to your imagination for now.) I am not a medical or mental health professional, just someone with a lifetime of personal experience.
azurelunatic's post about being prescribed a CBT workshop for insomnia is a great example. When I read it, I thought about my own sleep issues and how useless every behavioral approach -- both CBT-type approaches, and "sleep hygiene"-style approaches -- have been for it.
I have obstructive sleep apnea, so no behavioral approach can address the fact that untreated, I wake up more tired than I was when I went to bed, because I wake up many times an hour unable to breathe. But the main issue is that my body learned when I was a child that sleep was dangerous, and neither cognitive nor behavioral approaches can make my body unlearn that -- it's something I learned before I was developmentally able to use cognition or to reflect on my behavior.
As a child, I had an abusive parent who would force me to go to bed hours before I was actually ready to go to sleep, because she thought it was good for children to be on a regular sleep schedule. (Or because she wanted to control somebody and doing things to children that are generally believed to be for their own good is a socially acceptable way to do it. I don't really know.) So I learned that sleep meant lying in bed for hours, awake and intensely bored but not allowed to get up and do anything. When I got a little older I would get up and night and go into a walk-in closet in our apartment and read for as long as I could get away with it. When my mother figured out I was doing this, she unscrewed the light bulb. I learned to associate sleep, as well as going to bed early, both with an abusive parent who I knew was incapable of knowing what was good for me, and with hours of boredom and anxiety.
Therapists (and others) who apply CBT simplistically would tell me that the lasting, physical residue of these years are "cognitive distortions" that I need to reason my way out of. They would be wrong, because there's nothing distorted about mechanisms I learned in order to keep myself safe. Being awake is safer than being asleep in an environment that is dangerous for you, and for a child, there's nothing more dangerous than an environment that contains an alternately intrusive and inattentive caregiver and nobody else.
It's safe for me to relax now, and has been for the past twenty years, but because trauma changes your body in chemical and physical ways, just telling myself that won't make me go to sleep. I use chemical solutions to a chemical problem: medication. Maybe someday, I'll have had enough trauma therapy that I won't need it as often. But in the meantime, I'll be able to get enough rest and avoid some of the constant physical stress that arises from inadequate sleep.
CBT is politically attractive because it individualizes responsibility . Better to blame people's suffering on their own cognitive distortions, and teach them that they need to do work to overcome them (under capitalism, any solution that gives already-overworked people more work to do gets conferred with near-religious levels of praise), than to recognize that abuse culture harms people in long-lasting ways. If we recognized that many parenting practices widely considered to be non-abusive, or even helpful, in this culture are actually traumatic, we'd have to rethink a lot. Better to avoid confronting that by privatizing trauma and recasting it as individual pathology, ignoring the patterns in front of us.
Mental health is (I suspect) not the default state of human existence in the first place -- our brains are complicated and have too many failure modes for that. But in a society that depends on denial -- of the lasting effects of slavery (denial of the effects on white people, mostly), of the violence done by income inequality, and of the corrosiveness of toxic masculinity -- self-awareness is rebellion, and thus it's not surprising that to find therapies that foster it rather than providing a few tools to be economically productive while hurting inside, we often have to look outside the mainstream.