1. Trait diversity is traditionally seen as promoting species richness and ecosystem function. Species with dissimilar traits would partition available resources, increasing niche differences, facilitating coexistence and increasing ecosystem function.

2. Here we first show, using theory and simulations for light-limited phytoplankton, that combing photosynthetic pigments is indeed a necessary condition for coexistence and stimulates ecosystem function.

3. However, pigment richness does mostly not permit the coexistence of more than two species, and increases productivity at most 40\% compared to single-pigment communities. That is because blending in more pigments leads to coexistence of species with many pigments and therefore flat absorption spectra, which equalizes their fitness but decreases their niche differences. Similarly, seeding species with more variable size leads to an excess of large-celled species, which does not only decrease fitness differences, but also niche differences.

4. Empirical data and additional simulations suggest that pigment richness effects can be stronger during transient dynamics but inevitably weaken with time, i.e. pigment richness effects on species richness and function are likely short-lived.

5. Synthesis. Our results highlight the need to apply coexistence theory to understand the long-term effects of trait diversity on biodiversity and ecosystem function.