What does the Battle of Midway suggest? In a Naval engagement, involving Aircraft Carriers by both the opposing forces, the side with the most remaining Aircraft carriers, is victorious. This is obvious. So, how should these ships be used? They are basically a floating airbase. A small or medium Aircraft Carrier, can be dealth with, because the the planes carried by these, can be effectively parried by anti-aircraft missiles, on ships. This is, if the aircraft can be identified as a target, early enough. The aircraft has the advantage, because it's radar looks down, on ships. If an aircraft approaches the target at a sufficient altitude and distance, then it will perhaps identify the ship first.
If one looks at the history of Naval Aviation, the advantage of the Aircraft Carrier, has been of a constant particular nature. In the early days of Aircraft Carrier operation, the advantage was not clear to perception. But this advantage is known today, by how the vessel and it's weapons have developed.
No warship in the Second World War, was safe from air attack, because the ships never carried enough anti-aircraft weapons. The warship is an anti-ship platform first. I don't know about current warships. The Destroyer can be an effective anti-aircraft ship, but can the Aircraft Carrier defend itself? I believe the Nimitz class Super Carriers, are not immune to missile attack.