If you allow for some of the bluster and look past the sweeping generalisation, part of me thinks Dominic Cummings has a fair point here:
[Michael Barber’s] approach is based on the assumption that his team ‘always knows more about what “good” or “bad” looks like in other, similar organisations’ than officials and MPs do. This is the heart of the problem. It is inconceivable that Barber’s consultants could go into a brilliantly managed company like Apple and know more than the CEO about ‘what good or bad looks like in similar organisations’.
His team gets results because they are picking very low-hanging fruit— they are providing what should be minimal competence for people who do not know how to prioritise and are managerially incompetent.