The secretion of vesicles for intracellular transport often relies on the aggregation of specialized membrane-bound proteins into a coat able to curve cell membranes. The nucleation and growth of a protein coat is a kinetic process that competes with the energy-consuming turnover of coat components between the membrane and the cytosol. We propose a generic kinetic description of coat assembly and the formation of coated vesicles and discuss its implication to the dynamics of COP vesicles that traffic within the Golgi and with the endoplasmic reticulum. We show that stationary coats of fixed area emerge from the competition between coat growth and the recycling of coat components, in a fashion resembling the treadmilling of cytoskeletal filaments. We further show that the turnover of coat components allows for a highly sensitive switching mechanism between a quiescent and a vesicle producing membrane, upon a slowing down of the exchange kinetics. We claim that the existence of this switching behavior, also triggered by factors, such as the presence of cargo and variation of the membrane mechanical tension, allows for efficient regulation of vesicle secretion. We propose a model, supported by different experimental observations, in which vesiculation of secretory membranes is impaired by the energy-consuming desorption of coat proteins, until the presence of cargo or other factors triggers a dynamical switch into a vesicle producing state.