CBT works where people have a cause-effect conflict in their interpretation of an issue, and are open to analysing it as well. Other people may well have the same situation but resist almost all challenges that things may not be as they believe, but simply by being allowed to talk about it (person-centred therapy) will then start working things out themselves. So it really depends on the individual and the therapists are best off trying the likely method and switching (as I do) when they see it likely to work better using other ways.
Unlike the original methods based mainly on the work of Albert Ellis, although 'homework' was offered, it was not an essential or fundamental addition, whereas the fairly recent merger with behavioural therapy seems more a feature of the NHS than actual therapeutic private practice, which tends more to be a collection of the traditional methods and the latest ones, depending on the interests of the therapist, plus many courses only teach one method so the therapist has little choice but to stick to what they were taught.
But where incorrect attribution and confusion is at the heart of the problem it's the best place to start, adding tasks is not what we were taught as many people have enough tasks in their lives and tend to see more as something else to fail to do or get wrong, and must be made clear it is not for our benefit but theirs. I offer the odd suggestion as an option when I know it will help, and always make it 100% clear I used cognitive (or even earlier 'Rational-emotive therapy) and anything I suggest is an extra that may help speed up their progress, but as confusion and lack of information is a fundamental basis of the majority of personal problems I've come across, intellectually undoing them is the primary method of undoing them.