Senior leadership within the civil service is indeed key here. Now, to be clear, there are some very capable people at that level, and who justly hold their position in terms of the person's experience, aptitude, and intelligence. But (perhaps more than in the private sector) promotions at mid-manager level and above in the civil service rely as much on networking than in having in full measure these qualities or a record of delivery.
Those in higher positions but who are inept and inexperienced fall very easily for the out and out consultant bluffers, especially when these pander to held prejudices and simple beliefs. And because it's very difficult to evidence value in a non-profit organisation delivering public goods, any non-delivery or screw-ups is easy to cover up by the use of smoke and mirrors, including defection for blame
So yes, absolutely, those in headship positions (divisional directors an above) are ultimately the issue here.