Material efficiency is indispensable to reaching agreed targets for industry's energy and carbon emissions. Yet, in the EU, the energy- and emissions-saving potentials of this strategy continue to be framed as secondary outcomes of resource-related policies. Understanding why material efficiency has been overlooked as an energy/climate solution is a prerequisite for proposing ways of changing its framing, but existing studies have failed to do so. This paper fills this gap by triangulating interviews, policy documents and three policy theories: namely, historical and rational choice institutionalism, and multiple streams framework. Factors discouraging material efficiency as an energy and climate strategy include: difficulties in reframing the prevailing rationale to pursue it; the inadequacy of monitored indicators; the lack of high-level political buy-in from DG Energy and Clima; the ETS policy lock-in; uncoordinated policy management across Directorates; the lack of a designated industry lobby. Policy solutions are proposed. Before 2030, these are limited to minor amendments, e.g. guidance on embodied energy calculations or industry standards. Post-2030, more radical interventions are possible, such as introducing new fiscal drivers, re-designing the ETS emissions cap or benchmarks for allowances. This evidence suggests that the transition to a low-carbon industry will require Member State- and industry-level action.