Autonomous Vehicles (AVs) rely on individual perception systems to navigate safely. However, these systems face significant challenges in adverse weather conditions, complex road geometries, and dense traffic scenarios. Cooperative Perception (CP) has emerged as a promising approach to extending the perception quality of AVs by jointly processing shared camera feeds and sensor readings across multiple vehicles. This work presents a novel CP framework designed to optimize vehicle selection and networking resource utilization under imperfect communications. Our optimized CP formation considers critical factors such as the helper vehicles' spatial position, visual range, motion blur, and available communication budgets. Furthermore, our resource optimization module allocates communication channels while adjusting power levels to maximize data flow efficiency between the ego and helper vehicles, considering realistic models of modern vehicular communication systems, such as LTE and 5G NR-V2X. We validate our approach through extensive experiments on pedestrian detection in challenging scenarios, using synthetic data generated by the CARLA simulator. The results demonstrate that our method significantly improves upon the perception quality of individual AVs with about 10% gain in detection accuracy. This substantial gain uncovers the unleashed potential of CP to enhance AV safety and performance in complex situations.