Aircraft Carriers can be outfitted with technology to have AA Guns that fire just like ground based AA Guns. Only one per sea zone may fire, but it may fire at each attacking enemy aircraft.
CV was a poor defender for anti-aircraft. They relied on CAP to intercept incoming planes at lower altitude to intercept these and drive them away from the fleet. The Carrier created an umbrella of air cover to protect in this manner. It could not stand up to much of a fight and was the weakest in terms of AA capabilities in WW2.
IN modern times this changed but not in ww2. At midway 3 Japanese carriers were sitting ducks because the air cover was lost fighting off waves of incoming torpedo-bombers, and the carriers had the best Japanese equipment money could buy and it didn’t mean a thing because they were unescorted by cruisers and enough supporting ships.
A BB was a slower moving ship and was meant not to engage fighters but to engage surface ships and having the slower speed could only hope to surprise the enemy from nowhere or fight on equal terms against other battleships. Cruisers were some of the fastest ships and much better suited to fight airplanes by escorting fast carriers that were vulnerable.
The only thing the BB should have is a first strike attack against other surface warships.
Cruisers should move 3 with carriers and have a AA gun at planes hitting at 1 on the first round.
