I think CBT is training your mind to work together with you. Some of the most important things in getting your mind to cooperate (to achieve a result like better sleep), is A) believing that you can, B) Wanting it, and C) Putting in mental effort to achieve your goal. No, it's not a panacea and not guaranteed, but the science* is clearly there.
* Science - It works, bitches! (XKCD quote)