Please, RAM is not a CIWS. A CIWS is a gattling gun. RAM is a point defense missile.
The one point you simply fail to understand is that a fast moving missile can easily maneuver outside of the envelope of an intercepting missile like a standard or ram. A sudden pitch, for example, will put the faster missile beyond the reach of the slow missile -- EVEN IF THE SLOW MISSILE TRIES TO PITCH TOO SIMPLY BECAUSE THE FASTER MISSILE TRAVELS FURTHER!
Your explanation of the AEGIS system is grossly misleading to say the least. Your interceptors do not travel at the speed of light! They are even slower than the incoming missiles and therefore are at a huge disadvantage if the trajectory of the incoming missile cannot be accuracy predicted.
take a look at the predator and prey problem and you will see how one missile can catch up to another. Now, consider that you send two predators up there and you know exactly where the prey is going. Now, consider that the predator only has to get to a spot close enough to the predator to knock it off the path. You will see exactly how two intercepting missiles can intercept even faster targets. Again, the AShM is always going to face a greater task at searching for the ship than the other way around.
Same with guns, you know exactly where the missile is going to. In short burst, it can fire off at rate 70 rounds/s and the muzzle velocity for these things reach mach 3 or mach 4 depending on the round being used. And when the rounds reach the approximate target, they can either seek for the target or disperse into many small fragments and cover great area. You form these walls in the approximate area where the target is coming in. Net result, target gets pierced.