"beardedbruce, you have said that if any babies are killed by a nuclear weapon, the US will be obliged to destroy the entire world. So if even one nuclear armed missile gets through, NO lives will have been saved by this system."
The TREATY obligations are that if the US or any treaty signatory is attacked with WMD, the US will reply with WMD. If 1 missile is launched, we have a very high likelyhood of being able to intercept it. If 25 are launced, we have a good chance to eliminate 10 - 20 of them, reducing the loss of life ( in the US or our ally) by 40 - 80 %.
"It's not useful against these people if they have more nuclear armed missiles than we would be able to shoot down, and there's absolutely no guarantee that such would not be the case"
Recall that a single missile from a Nuclear power ( China, Russia, etc) can have 8 - 12 MIRV warheads, probably on the order of 250Kt each. A missile from a terrorist group or rogue nation would probably have one warhead, in the 20 -50 KT range.
It seems likely that a rogue nation or terroruist group would have access to a limited number of systems, while the nations that you claim would be threatened because they would lose their deterrence would have the number to overwhelm the defensive system- Thus it DOES NOT destabilize the balance of power, just defend against rogue states and terrorist groups.