Central bank independence (CBI) has often been presented as a superior institutional arrangement demonstrated by economists in the 1980s for achieving a common good in a non-partisan manner. In this article, we argue that this view must be challenged. First, research in the history of economic facts and thought shows that the idea of CBI is not new, and was adopted under peculiar socio-historical conditions, in response to particular interests. Rather than an indisputable progress in economic science, CBI is the foundation for a particular configuration of the monetary regime, perishable like its predecessors. Secondly, we argue that the simplistic case imagined by the CBI theory (the setting of a single interest rate disconnected from political pressures) is long overdue. For nearly two decades, central banks have been increasing their footprint on the economy, embarking on large asset purchase programs and adopting macroprudential policies. This pro-activism forces independent central banks to constantly address new distributional - and therefore political - issues, leading to a growing number of criticisms of their actions with regard to inequality or climate change. This growing gap between theory and practices makes plausible a further shift of the institutional arrangement towards a democratization of monetary policy.