The Michaelis-Menten equation provides a hundred-year-old prediction by which any increase in the rate of substrate unbinding will decrease the rate of enzymatic turnover. Surprisingly, this prediction has never been tested experimentally nor scrutinized using modern theoretical tools. We show that unbinding may also speed up enzymatic turnover, spotlighting the fact that its actual role in enzymatic catalysis remains to be determined experimentally. We analytically construct the unbinding phase space and identify four distinct categories of unbinding: inhibitory, excitatory, superexcitatory, and restorative. A transition in which the effect of unbinding changes from inhibitory to excitatory as the substrate concentration increases, and an overlooked tradeoff between the speed and efficiency of enzymatic reactions, are naturally unveiled as a result.