Cities are facing severe traffic-related problems causing emission thresholds to be exceeded. All around the world, city center access restriction policies are being tested to foster the adoption of electric commercial vehicles (ECVs) and to reduce emissions. In this paper, we analyze the impact of a broad spectrum of such policies on fleet logistics. We develop an algorithm that solves large real-world instances and mimics a fleet operator's decisions. We present a multigraph setting to handle trade-offs between cheapest and quickest paths. Further, we consider the cost structure of heterogeneous fleets. Our results provide the basis for municipalities to use decision support to identify suitable city center access restriction policies. We show which pricing schemes and restriction policies encourage the sustainable usage of ECVs in logistics fleets. We further show which policies have a negative impact on fleet operations, e.g., by increasing the traveled distance or emissions.