Strain-rate softening has been associated with a wide variety of material instabilities, from the Portevin-Le Chatelier effect in metal alloys to stick-slip motion in crust faults. Dynamic instability patterns have been recently discovered in brittle porous media: diffused, oscillatory, and erratic compaction. Using model simulations inspired by experiments with puffed rice, we question the link between these dynamic patterns and strain-rate sensitivity in such media. An important feature of our model is that it can recover strain-rate softening as an emergent phenomenon, without imposing it a priori at its microstructural scale. More importantly, the model also demonstrates that the full range of dynamic patterns can develop without presenting macroscopic strain-rate softening. Based on this counterexample model, we therefore argue that strain-rate softening should not be taken as a necessary condition for the emergence of instability patterns. Our findings in brittle porous media have implications on models that require strain-rate softening to explain earthquake and metal alloy instabilities.