The brain represents the world through the activity of neural populations; however, whether the computational goal of sensory coding is to support discrimination of sensory stimuli or to generate an internal model of the sensory world is unclear. Correlated variability across a neural population (noise correlations) is commonly observed experimentally, and many studies demonstrate that correlated variability improves discriminative sensory coding compared to a null model with no correlations. However, such results do not address whether correlated variability is for discriminative sensory coding. If the computational goal of sensory coding is discriminative, then correlated variability should be optimized to support that goal. We assessed optimality of noise correlations for discriminative sensory coding in diverse datasets by developing two novel null models, each with a biological interpretation. Across datasets, we found correlated variability in neural populations leads to highly suboptimal discriminative sensory coding according to both null models. Furthermore, biological constraints prevent many subsets of the neural populations from achieving optimality, and subselecting based on biological criteria leaves discriminative coding performance suboptimal. Finally, we show that optimal subpopulation are exponentially small as the population size grows. Together, these results demonstrate that the geometry of correlated variability leads to highly suboptimal discriminative sensory coding.