The role of government in fostering HE’s contribution to societal cooperativeness is, in present conditions of high demand, contested both politically and ideologically. Although devolution of decision taking to universities is widely apparent, four types of strong influence remain in government use: mandates, funding incentives, investment in capacity-building, and overall system adjustment. These have fostered changes in the HE policy agenda from the outcomes espoused in the foundational Robbins Report namely: skilling (not prioritized), general powers of the mind, the advancement of learning, and a shared culture of citizenship. Over-skilling now grows, and leaves difficult policy questions such as: occupational filtering down, student debt and loan servicing, bureaucratic drift with related transaction costs, and decline in education standards. Considering what a university is good for, as opposed to good at, is a challenge for many policy makers.