During clathrin-mediated endocytosis, dozens of proteins assemble into an interconnected network at the plasma membrane. As initiators of endocytosis, Eps15 and Fcho1/2 concentrate downstream components, while permitting dynamic rearrangement within the budding vesicle. How do initiator proteins meet these competing demands? Here we show that Eps15 and Fcho1/2 rely on weak, liquid-like interactions to catalyze endocytosis. In vitro, these weak interactions promote the assembly of protein droplets with liquid-like properties. To probe the physiological role of these liquid-like networks, we tuned the strength of initiator protein assembly in real time using light-inducible oligomerization of Eps15. Low light levels drove liquid-like assemblies, restoring normal rates of endocytosis in mammalian Eps15 knockout cells. In contrast, initiator proteins formed solid-like assemblies upon exposure to higher light levels, which stalled vesicle budding, likely owing to insufficient molecular rearrangement. These findings suggest that liquid-like assembly of initiator proteins provides an optimal catalytic platform for endocytosis.