You have it completely backwards. If AH modeled AA realistically, you'd rarely get near the CV.
ack-ack
I was going to post some numbers, but my stupid Chrome crashed and I lost it - however I was going to show the AAA armament for the Battle of Midway (USS Yorktown) compared to the USS Franklin in late 44, if we had a Late war compliment of AAA then you wouldn't be getting near a CV period.
For example we don't have CLAA's which were designed as AAA platforms, Battleships such as IOWA's were a floating arsenal with 20x 5in/38 cal guns, some 80x 40mm Bofers and 50x 20mms, even the Late war carriers were a beast to reckon with.
Interesting to note the wartime upgrade, Carriers and other warships were not designed entirely to stop Air attacks at the start of the war, however
if you look at the gradual increase of AAA firepower, in 1945 it was just pure nasty, with good reason too - surface ships were not much a threat the entire war (as they were from the start in which ships were feared) for example the Mogami class Cruiser, the US built the Brooklyn-class light cruiser to combat it.
Anyhow, I am thankful we don't have the possible floating arsenal that was available in 1945.