Stability of microbial cooperation through common goods is susceptible to cheating. Evidence suggests that cheating plays a less prominent role in many natural systems than hitherto predicted by models of eco-evolutionary dynamics and evolutionary game theory. While several cheater negating factors such as spatial segregation have been identified, most consider single-nutrient regimes. Here we propose a cheater-suppressing mechanism based on previous experimental observations regarding the biochemical trade-off between growth speed and delay in switching to alternative nutrients. As changing the nutrient source requires redistribution of enzymatic resources to different metabolic pathways, the advantage in speed is offset by lower agility due to longer time required for resource re-allocation. Using an in silico model system of sucrose utilisation by Saccharomyces cerevisiae, we find that a trade-off between growth rate and diauxic lag duration can supress cheaters under fluctuating nutrient availability and thereby stabilise cooperation. The resulting temporal dynamics constrain cheaters despite their competitive benefit for the growth on the primary nutrient via avoided public goods synthesis costs. We further show that this speed-agility trade-off can function in synergy with spatial segregation to avoid the collapse of the community due to the cheaters. Taken together, the growth-agility trade-off may contribute to cheater suppression in microbial ecosystems experiencing fluctuating environments, such as plant root microbiota and gut microbiota.