Sleep is an active biochemical process, orchestrated in different ways at different times across the brain. Its initiated by, amongst other things, a release of prostaglandin D2.
Sleep is not a passive letting go. If you are fixated on some thoughts or feelings that block sleep, then dealing with those might help. So in mild situational insomnia, anything that makes you drowsy or relaxed might help, so CBT might have some limited value.
I am far too out of date on the science of circadian regulation to be sure of much, but there are multiple chemical clocks in different parts of the body, and suprachiasmatic nucleus regulation of sleep was known to be regulated by at least fifteen different things, including chemical concentrations, some decades back. Now we know there might be a second regulation location in the brain stem, but I know nothing about that. Its not simple.
CBT might help you let go and therefore relax, but if the biochemistry of sleep is perturbed it will do nothing.
Insomnia is like stage one sleep disorder, based on a listing I read years ago. Stage or rank 5 is non-24 hour disorder, typically attributed to blindness due to loss of light entrainment. I have it and so do many with ME I have talked to over the years.
I also have what I consider two further stages at times. I call the next aggressive non-24, where sleep does not move an hour a day, but 4 or 8 or 12 hours a day.
After that is the one I find the worst, total loss of circadian rhythm. I sleep when I sleep, for short periods, randomly, with no obvious pattern. If I try to go too long without sleep its a problem.
To complicate things I get something I call non-narcolepsy. I feel an overwhelming need for sleep that hits suddenly, but unlike narcolepsy proper I can fight it ... if I do nothing else but fight it. That renders me incapacitated. Much better to just go sleep.
We also have circadian reversal at some prevalence, typically only seen in African sleeping sickness, I know several ME patients who have it including me. It might be related to alterations in PGD2, as suggested for African SS. Prostaglandin D2 might be related, though it might have other causes. If deficiency of prostaglandins is involved then it might also relate to salicylate sensitivity, which in turn is related to oxidative stress and glutathione.
I am now in my 55th year of ME. Some of these issues took decades to show up. I got hypersomnia in the earlier years but it gradually got displaced by various issues preventing sleep.
CBT tries to be a one stop shop, applying simplistic methods to complex problems, and if its like other applications of CBT research we are aware of its extremely unreliable research, and sometimes verging on scientific misconduct, and in at least one case actual scientific misconduct. As others have said, its an admission of failure. Do CBT because we don't have a clue how to fix what is wrong, or even what the mechanisms are!