Flow instabilities driven by the dissipative nature of particle–particle interactions have been well documented in granular flows. The bulk of previous studies on such instabilities have considered the impact of inelastic dissipation only and shown that instabilities are enhanced with increased dissipation. The impact of frictional dissipation on the stability of grains in a homogeneous cooling system is studied in this work using molecular dynamics (MD) simulations and kinetic-theory-based predictions. Surprisingly, both MD simulations and theory indicate that high levels of friction actually attenuate instabilities relative to the frictionless case, whereas moderate levels enhance instabilities compared to frictionless systems, as expected. The mechanism responsible for this behaviour is identified as the coupling between rotational and translational motion. These results have implications not only for granular materials, but also more generally to flows with dissipative interactions between constituent particles – cohesive systems with agglomeration, multiphase flows with viscous dissipation, etc.