In planetary nebulae (PNe), abundances of oxygen and other heavy elements derived from optical recombination lines are systematically higher than those derived from collisionally excited lines. We investigate the hypothesis that the destruction of solid bodies may produce pockets of cool, high-metallicity gas that could explain these abundance discrepancies. Under the assumption of maximally efficient radiative ablation, we derive two fundamental constraints that the solid bodies must satisfy in order that their evaporation during the PN phase should generate a high enough gas-phase metallicity. A local constraint implies that the bodies must be larger than tens of meters, while a global constraint implies that the total mass of the solid body reservoir must exceed a few hundredths of a solar mass. This mass greatly exceeds the mass of any population of comets or large debris particles expected to be found orbiting evolved low- to intermediate-mass stars. We therefore conclude that contemporaneous solid body destruction cannot explain the observed abundance discrepancies in PNe. However, similar arguments applied to the sublimation of solid bodies during the preceding asymptotic giant branch phase do not lead to such a clear-cut conclusion. In this case, the required reservoir of volatile solids is only one ten-thousandth of a solar mass, which is comparable to the most massive debris disks observed around solar-type stars, implying that this mechanism may contribute to abundance discrepancies in at least some PNe, so long as mixing of the high-metallicity gas is inefficient.