Margin requirements protect a central counterparty (CCP) and its users against potential losses generated by the default of any of its members. They have several components, one of them being the initial margin requirement, which is typically calculated using a market risk model to estimate the potential future exposure of each member's portfolio. By definition, market risk models - whether for centrally cleared or bilateral cleared trades - have to be sensitive to changes in market risk and, as a consequence, when market risk increases, initial margin requirements will tend to increase. After the 2008 crisis, regulators had concerns about this becoming procyclical, in the non-technical sense of amplifying financial stress. As a result, CCPs have put in place different procyclicality mitigation tools. But when the markets are stressed and participants face larger margin calls, like in the recent events of March 2020, interest on the procyclicality of initial margin models seems renewed. In this paper we argue that the focus on initial margin models is misplaced. First, margin calls are largely driven by variation margin, not initial margin. Second, the inherent risk sensitivity of margin models, the stochastic nature of the problem, and the different trade-offs involved, constrain what can be achieved with model calibration. We illustrate why this is the case by empirically testing the performance of standard initial margin models during the recent March 2020 events and quantifying the different trade-offs. Therefore, if procyclicality of IM has been mitigated to the limit of what is practical and prudent, but fragilities in the system persist, how should these be addressed and who is responsible for addressing them? We argue that, since the ultimate objective is to minimize systemic propensities to adverse feedback loops, these questions demand a systemic perspective, focusing on the interactions between participants rather than on a single node.