Actually AARHE was the first to use this idea. Back in 2004-5
Each ship has an anti-aircraft capability
Cruiser 3
Battleship 2
Destroyer 1
Carrier 2
Ships can either defend using normal combat values or roll one of these or less and the hit is scored on a plane.
Then i extrapolated the idea for Cruisers and Commander Jennifer incorrectly used the idea for Battleships, which historically didn’t make sence. The other thing was Cruisers are too costly at 12, so to give them a natural AA capability @1 for the first round,and reduce the cost to 11 might balance the unit.
Battleships are balanced and don’t need a AA, so its not only out of balance to have it but it is also not realistic
Cruisers didn’t have the displacement for large guns. These are fast and long range escort ships. They became AA gun platforms because AA are light and they can keep up with Carriers, unlike Battleships.
Battleships are heavy duty battle units to engage other ships in surface combat. They have sufficient displacement for many larger guns and not so much for lots of little AA guns. Battleships need to be protected by escorts ( destroyers and cruisers).
Cruisers had the most AA guns on average ( as measured by tons and space) then any other unit. They were the best escorts for Carriers and Battleships because they had speed, so they got the AA guns.
Destroyers had mostly an Anti submarine role, but cruisers had this too. AARHE was also the first one to introduce cruisers and give them ASW capability at 1:1 basis, like Destroyers.