Why weren t the German defenses at Omaha Beach knocked out by airpower and the naval bombardment?
Because of concern about hitting Allied troops, Allied bombers were ordered to delay their drop point a couple of seconds inland. Consequently all their bombs fell well behind the German defenses. The naval bombardment was curtailed in attempt to preserve the element of surprise. However, a key element to the U.S. troops getting off the beach at Omaha were the U.S. Navy destroyers that closed on the shore until there were literally only a couple of inches of water beneath their keel. At point blank range they dueled with the German gun emplacements and cleared exits from the beach.
