Developing autonomous vehicles that can navigate complex environments with human-level safety and efficiency is a central goal in self-driving research. A common approach to achieving this is imitation learning, where agents are trained to mimic human expert demonstrations collected from real-world driving scenarios. However, discrepancies between human perception and the self-driving car's sensors can introduce an $\textit{imitation}$ gap, leading to imitation learning failures. In this work, we introduce $\textbf{IGDrivSim}$, a benchmark built on top of the Waymax simulator, designed to investigate the effects of the imitation gap in learning autonomous driving policy from human expert demonstrations. Our experiments show that this perception gap between human experts and self-driving agents can hinder the learning of safe and effective driving behaviors. We further show that combining imitation with reinforcement learning, using a simple penalty reward for prohibited behaviors, effectively mitigates these failures. Our code is open-sourced at: https://github.com/clemgris/IGDrivSim.git.