Understanding the effects of evolution on emergent population properties such as intrinsic growth rates, species abundances or resilience is not only a key theoretical question, but has major empirical implications, for instance in conservation, agroecology and invasion ecology. Evolution can also lead to polymorphism based on niche differentiation among different phenotypes. The present article has three aims. First, we clarify the evolutionary scenarios allowing for optimization of population growth rate and abundance. Second, we relate the eco-evolutionary emergence of polymorphism to the niche-overlap and fitness-ratio sensu coexistence theory. Third, we discuss whether properties of polymorphic populations can be optimized due to niche-displacement among phenotypes. We revisit previous theoretical results on eco-evolutionary optimization and link them with our Lotka-Volterra framework. Depending on how the traits under selection affect species intrinsic growth rates or ecological interactions, we uncover three scenarios, ranging from the optimization of all three properties to no optimization and link evolutionary dynamics to coexistence theory. Optimization is, in general, incompatible with niche differentiation sensu coexistence theory and, therefore, with the emergence of polymorphism. Niche displacement between resident and mutant phenotypes, and potentially polymorphism, only arise when we do not expect optimality to hold. Finally, we show how our approach can be generalized to coevolutionary scenarios. In the discussion, we propose biological scenarios and traits that may fall into our three scenarios. Although it is possible to find traits for which optimality is expected, for the majority of the cases optimization arguments do not hold. We also provide practical applications of our results in conservation, agroecology, harvesting and invasion ecology.