For decades, academic biologists have advocated for making conservation decisions in light of evolutionary history. Specifically, they suggest that policy makers should prioritize conserving phylogenetically diverse assemblages. The most prominent argument is that conserving phylogenetic diversity (PD) will also conserve diversity in traits and features (functional diversity [FD]), which may be valuable for a number of reasons. The claim that PD-maximized (“maxPD”) sets of taxa will also have high FD is often taken at face value and in cases where researchers have actually tested it, they have done so by measuring the phylogenetic signal in ecologically important functional traits. The rationale is that if traits closely mirror phylogeny, then saving the maxPD set of taxa will tend to maximize FD and if traits do not have phylogenetic structure, then saving the maxPD set of taxa will be no better at capturing FD than criteria that ignore PD. Here, we suggest that measuring the phylogenetic signal in traits is uninformative for evaluating the effectiveness of using PD in conservation. We evolve traits under several different models and, for the first time, directly compare the FD of a set of taxa that maximize PD to the FD of a random set of the same size. Under many common models of trait evolution and tree shapes, conserving the maxPD set of taxa will conserve more FD than conserving a random set of the same size. However, this result cannot be generalized to other classes of models. We find that under biologically plausible scenarios, using PD to select species can actually lead to less FD compared with a random set. Critically, this can occur even when there is phylogenetic signal in the traits. Predicting exactly when we expect using PD to be a good strategy for conserving FD is challenging, as it depends on complex interactions between tree shape and the assumptions of the evolutionary model. Nonetheless, if our goal is to maintain trait diversity, the fact that conserving taxa based on PD will not reliably conserve at least as much FD as choosing randomly raises serious concerns about the general utility of PD in conservation.