Every fire control can target one target every 5 second increment.  So if your AMM launchers can fire every 5 seconds, you might want to have a few FCs so that none of your launchers are sitting idle as each enemy missile salvo (which are the missiles fired by one FC) counts as a seperate target.

Attacks are rolled salvo vs salvo, and a salvo's attacks are rolled all at once; once an AMM salvo is committed, all the missiles are lost no matter what. So it's pretty rare to recoverably waste AMMs.  The most common wastage scenario is on the last 5s of a missiles approach; if the missile is higher speed than your AMMs, it moves first, and hits your ship before the AMMs can hit it, causing the AMMs to lose target and self-destruct.

So, digging in to AMM design, I note they need a lot of fire controls to get even the option of shooting one AMM per incoming missile.  But perhaps that isn't necessary.

My understanding of the mechanics is that if you are shooting, say, five AMMs at a missile in an incoming volley, and the first AMM takes it out, the succeeding four AMMs will continue to the location of their last target, and lo and behold there will be a whole bunch more targets for them.  If the onboard sensors can target missiles within say 10,000km, won't that be enough?

There would be some slight performance cost, as the sensor's mass would come at the expense of agility, but the advantage in terms of less missile overkill wastage or less mass spent on extra fire controls seems to be worth it, at least at some tech levels.

So an anti-missile escort could have a long-ish ranged fire control, so it could fire in antifighter or antiship mode, and some short ranged fire controls, but it could still expect to be able to thin out incoming missile waves with the long ranged fire control (assuming a forward sensor to detect the incoming waves early, perhaps).

So am I missing something in the mechanics, or is it simply too difficult to shoehorn even a point blank antimissile sensor into a size 1 missile?