For many years, controversy has surrounded the use of biofilm models to describe the distribution of microbial biomass in natural or artificial porous media. This use is often advocated on the basis of the relative mathematical simplicity of the biofilm concept, and of the widespread availability of analytical solutions or numerical implementations. However, microscopic observations consistently point to a patchy, rather than homogeneous, distribution of microorganisms at the pore scale in many porous media of interest, even under conditions of severe bioclogging. Also, bioclogging models involving biofilms tend to underpredict the extent of permeability reductions in all be the coarse-textured materials. In this context, computer simulations described in the present article show that some of the limitations of biofilm models to describe the bioclogging of porous media are linked to the common constitutive assumption that biofilms are impermeable, that is, that nutrient transport occurs through the biofilms only by molecular diffusion. When this restriction is alleviated and liquid flow is allowed in the biofilms, the level of bioclogging achievable by a given biomass is very significantly increased and is comparable to that observed in experiments. In addition, the distribution of microorganisms becomes patchy and exhibits a self-organized periodic pattern with pores either entirely filled with biomass or without any biomass at all, again similar to published microscopic observations. These results suggest that biofilm models should not be ruled out a priori for the quantitative description of bioclogging in porous media, as long as biofilms are allowed to be permeable.