Strange metals, an enigmatic state of matter found in many strongly correlated materials, still defy a clear and unified understanding. Their phenomenology is incompatible with normal Fermi liquids. Despite the ubiquity of strange metals, many basic questions remain unsettled, in particular, whether intrinsic strange metals, i.e., ones without disorder, exist. Here we present a novel approach to intrinsic strange metals where phenomena like ω/T scaling and a linear-in-T resistivity arise from collective short-ranged fluctuations. We focus on heavy-fermion metals, where strange-metal behavior routinely emerges in the quantum-critical region of so-called Kondo-breakdown quantum-critical points. We find ω/T scaling for several susceptibilities and strange-metal behavior for the optical conductivity and resistivity. Importantly, this behavior arises from dominant vertex contributions rather than single-particle decay.