Universal collisions describe the reaction of molecules and atoms as dominated by long-range interparticle interactions. Here, we calculate the universal inelastic rate coefficients for a large group of ultracold polar molecules in their lower ro-vibrational states colliding with one of their constituent atoms. The rate coefficients are solely determined by values of the dispersion coefficient and reduced mass of the collisional system. We use the ab initio coupled-cluster linear response method to compute dynamic molecular polarizabilities and obtain the dispersion coefficients for some of the collisional partners and use values from the literature for others. Our polarizability calculations agree well with available experimental measurements. Comparison of our inelastic rate coefficients with results of numerically exact quantum-mechanical calculations leads us to conjecture that collisions with heavier atoms can be expected to be more universal.