@Charlie
But you miss their core design principle: To be as light and as fast as possible in order to keep up with all but the fastest missiles. Sure, I could go lasers for more range, but that adds on a good 140 tons at that tech level, halving the number of fighters I can carry and crippling their speed advantage. The same thing would be argued if I increased the size of the BFC to maximize their to hit. They rely on being able to keep up with all but the fastest missiles so that they can attack during multiple phases.
Around this tech level, for half a HS less than the hanger, you can put in a quad gauss turret tracking at 20k with a base hit rate of 67%. Note that this does *not* include the non-trivially sized BFC that you'll need to properly target the missiles, but lets be generous and give the design advantage to the system that's thought superior. If we throw in the BFC that I designed for my carrier we're looking at an additional 3HS and an accuracy of 93% at 10k. Let's also assume that the missiles are moving at 20k, as that's a fairly realistic expectation at this tech level, with a reload of 30sec. Oh, and because I'm lazy, I'll just fix the gauss rate of fire at four.
So, with all that said, my fighters are looking at three to four phases of combat to the turret's one due to the 30sec reload.
Fighters: With three phases of combat, we're looking at 3 * 32 * 0,086 for their expected number of hits. With four, it'd simply be 4 * 32 * 0,086. (Phases of combat * shots per phase * accuracy, if it wasn't clear).
Turret: We're looking at roughly 16 * 0,62.
Feeling too lazy to do some arithmetic, so I'll just simplify the three to 16 * 0,51 for the fighters@3, 16 * 0,68 for fighters@4, and 16 * 0,62 for the turret.
This is, of course, a simplification of the combat as other factors are not included for the sake of simplification. There's no missile tracking bonus, which is something that would favor the turret slightly. The missiles are all assumed to be in a single salvo, which favors the turret heavily. In a more realistic setting, even if the fighters were barely half as effective in my simplified model as the turret, they may well take down more missiles if the turret is forced to fire on a salvo with only four missiles in it. ECM/ECCM haven't been included at all. There are probably other influencing factors that I haven't included here, but this should get the point across that the fighters hold up well against the turrets on paper.
@general
The thing is, I can already accomplish what I want to do (intercept the missiles), but it's a complete pain in the ass as I'm forced to visually estimate, without a grid, where the missiles will end up after their phase of movement. Combine that with the fact that I'll have to be sending many squads of fighters to that location (Each "carrier" (Escort is a better name) only carries eight) and I'll be doing several minutes of tedious micromanagement to pull off a single phase of anti-missile combat.