The reason is simple. The P-38 was a fighter, not an aerobatic sportplane. Combat does not use slow maneuvers since hitting a slow-moving target is EASY. So the P-38 nosewheel door was not designed for extended lifting airflow. Sustinaed inverted flight was never anticipated and would be, at best, a rather stupid maneuver if you aren't in an airshow. The P-38 was not designed for inverted flying at airshows.