Enzymes speed up reactions that would otherwise be too slow to sustain the metabolism of self-replicators. Yet, most enzymes seem only moderately efficient, exhibiting kinetic parameters orders of magnitude lower than their expected physically achievable maxima. Here, we question how these parameters evolve using a mechanistic model where enzyme efficiency is a key component of individual competition for resources. We show that kinetic parameters are under strong directional selection only up to a point, above which enzymes appear to evolve under near-neutrality. A majority of kinetic parameters compiled elsewhere do spread onto this plateau. Nonetheless, using a population genetics model that includes genetic drift and mutational biases, we show that this is a very unlikely outcome of evolution on a common landscape, as even very moderate biases towards lower efficiency should prevent the occurrence of such a diversity. Instead, differences between species, and within a species between metabolic pathways and the reactions to perform, should be involved. Our results point to drift playing an important role, along with the kinetics of nutrient transporters, the tolerance to high concentrations of intermediate metabolites, and the reversibility of reactions. Enzyme concentration also shapes selection on kinetic parameters, suggesting that the joint evolution of concentration and efficiency, facilitated by the plateau, should matter. Interestingly, the position of an enzyme along the metabolic pathway is not key for its evolution, contrasting with the prediction of models assuming that fitness depends on a precise level of flux control, rather than on competitive abilities.