Here is my take on this problem. Someone mentioned why should we care about putting AA on capital ship while it's nowhere near as effective as using Flak frigate, that's half of the problem.
Right now Fighter/Bomber is too insignificant of a threat to Capital ships that they really matter a damn. Why should I chase down a squadron when I can take out the Mother body much easier to begin with. There are too few squadrons and they do little damage to the capship to make they really pose a threat. Frankly right now it's not that big of a much difference whether the cap ships have AA or not
My proposal is to make Bomber more lethal (about 1/3-1/2 more powerful), and in turn give the Capital ships some limited AA defense, I would say about 1/5 - 1/3 the capacity of a Flak Frigate. This means the capships will still need Flak Frigates to compose a serious defense, a lone Capship can be swarmed by bombers if it's careless. However it also offer a decrease of defensive against bombers. It's not much by individual but say a group of 3 Capital Ship should have enough defense to fence of a bomber rush. Since right now not having AA on capital ship feels too much like an artificial handicap, and that's an immersion killing point.
I have another quirk about this, if possible I'm willingly trade of the Hangar space on capital ships for AA defense. First, it's more realistic. Second, it emphasizes better the variety between ships functionality, especially that of the carriers because right now their low number of squadron, low power of their squadron and actually decent fire power of themselves make the role of the carriers not as distinguishable as I feel they should be.
Maybe the carriers should have more squadron, at the sametime remove the squadron from other capital ships but give them raw AA defense, and make the squadron more powerful. This may be a better combination.