The influence of the nucleation energy barrier on the capillary-driven coarsening of faceted crystals that exchange material by diffusion is quantified. Our calculations are based on the assumption that the transport of material between particles must happen in series with the nucleation of partial layers on flat facets. Using a numerical model based on this idea, we simulate the time evolution of distributions of crystals that are made up of perfect faceted crystals (without step-producing defects), crystals containing step-producing defects, and mixtures of the two types. We find that the coarsening of a distribution containing only perfect faceted crystals is arrested at a size where the nucleation energy barrier becomes prohibitive. This critical size ranges from a few nanometers to several hundred nanometers, depending on material parameters and experimental conditions. When a small fraction of the crystals have step-producing defects (for these crystals the nucleation energy barrier vanishes), they can grow to large sizes at the expense of the perfect crystals and a bimodal grain size distribution is created. Based on these results, we hypothesize that when abnormal coarsening is observed in nature, it results from the presence of a small number of crystals with step-producing defects.