While most biodiversity and ecosystem functioning (BEF) studies have found positive effects of species richness on productivity, it remain unclear whether similar patterns hold for marine phytoplankton with high local richness. We use the continuous trait‐based modelling approach, which assumes infinite richness and represents diversity in terms of the variance of the size distribution, to investigate the effects of phytoplankton size diversity on productivity in a three‐dimensional ocean circulation model driven by realistic physics forcing. We find a slightly negative effect of size diversity on primary production, which we attribute to several factors including functional trait‐environment interactions, flexible stoichiometry and the saturation of productivity at low diversity levels. The benefits of trait optimisation, whereby narrow size distributions enhance productivity under relatively stable conditions, tend to dominate over those of adaptive capacity, whereby greater diversity enhances the ability of the community to respond to environmental variability.