Is Cognitive Behavioral Therapy good for mood & stress?

Yes — the evidence for this is strong. Beyond its well-established efficacy for anxiety and depression, CBT has strong, replicated randomized-trial evidence for chronic insomnia — a flagship meta-analysis in Annals of Internal Medicine, later refined by a component network meta-analysis identifying which parts of the therapy drive benefit — with further meta-analyses confirming gains in insomnia patients with comorbid mental disorders or chronic disease, and improved quality of life. That's reflected in an evidence score of 90/100 for its role in mood & stress, drawn from 7 studies, with an estimated impact on longevity rated substantial (78/100).