What is the minimal set of cell-biological ingredients needed to generate a Golgi apparatus? The compositions of eukaryotic organelles arise through a process of molecular exchange via vesicle traffic. Here we statistically sample tens of thousands of homeostatic vesicle traffic networks generated by realistic molecular rules governing vesicle budding and fusion. Remarkably, the plurality of these networks contain chains of compartments that undergo creation, compositional maturation, and dissipation, coupled by molecular recycling along retrograde vesicles. This motif precisely matches the cisternal maturation model of the Golgi, which was developed to explain many observed aspects of the eukaryotic secretory pathway. In our analysis cisternal maturation is a robust consequence of vesicle traffic homeostasis, independent of the underlying details of molecular interactions or spatial stacking. This architecture may have been exapted rather than selected for its role in the secretion of large cargo.