Building robust 3D perception for self-driving still relies heavily on large-scale data collection and manual annotation, yet this paradigm becomes impractical as deployment expands across diverse cities and regions. Meanwhile, modern cities are increasingly instrumented with roadside units (RSUs), static sensors deployed along roads and at intersections to monitor traffic. This raises a natural question: can the city itself help train the vehicle? We propose infrastructure-taught, label-free 3D perception, a paradigm in which RSUs act as stationary, unsupervised teachers for ego vehicles. Leveraging their fixed viewpoints and repeated observations, RSUs learn local 3D detectors from unlabeled data and broadcast predictions to passing vehicles, which are aggregated as pseudo-label supervision for training a standalone ego detector. The resulting model requires no infrastructure or communication at test time. We instantiate this idea as a fully label-free three-stage pipeline and conduct a concept-and-feasibility study in a CARLA-based multi-agent environment. With CenterPoint, our pipeline achieves 82.3% AP for detecting vehicles, compared to a fully supervised ego upper bound of 94.4%. We further systematically analyze each stage, evaluate its scalability, and demonstrate complementarity with existing ego-centric label-free methods. Together, these results suggest that city infrastructure itself can potentially provide a scalable supervisory signal for autonomous vehicles, positioning infrastructure-taught learning as a promising orthogonal paradigm for reducing annotation cost in 3D perception.