CDM 2007 competence is about being able to do your work safely, not endanger others and meet the legal health and safety requirements. There is justifiable emphasis on competence, because competent people are generally recognised as safer.
The duties in the Regulations work both ways. People making appointments have to take reasonable steps to make sure those appointed are competent for what they are expected to do. Likewise, those accepting such appointments should only do so if they are competent to undertake the activity.