Just how effective do you want to make the starbase AA defenses? If the enemy bomber swarms are so effective as to overwhelm everything else, just what kind of effect would any reasonable (as in not stupidly powerful) amount of starbase AA have? Even the Beta 1 titans folded like cardboard against sufficient numbers of strikecraft.
Yes, I happen to have played against advent before, and I do know both human advent players and AI like to use drone hosts and carrier caps. This was the main reason why in defensive situations I picked the habit of placing two to four hangar bays in close proximity to my starbases. Other than that it should be more important to take out the sources of the spam instead of trying to completely nullify the effect of those strikecraft. Which, again, should be done by the protective fleet. In your own or neutral gravity wells close to enemy territory something like a protective fleet should exist, or at least be closeby.
Edit: Also, the player using that large number of carriers had to invest lots of time and resources into producing all those ships, where is the worth in investing into carriers if their only weapon was shredded by a lone starbase? Ogrovs are a lot cheaper and kill starbases easily. Of course the carriers kill everything else, too. But looking at their supply and resource cost they should do that.
