Symmetric distribution properties such as support size, support coverage, entropy, and proximity to uniformity, arise in many applications. Recently, researchers applied different estimators and analysis tools to derive asymptotically sample-optimal approximations for each of these properties. We show that a single, simple, plug-in estimator-profile maximum likelihood (PML)is sample competitive for all symmetric properties, and in particular is asymptotically sampleoptimal for all the above properties.