And that's the thing about GMD and other BMD systems: they aren't going to be much use against a full nuclear exchange. But what they are great for is the ragged second strike scenario. If the US goes first in a nuclear war and catches Russia/China off guard, it's possible for most of their hundreds of missiles to be taken out in their silos. And they might only be able to answer with a dozen or so missiles in response, which GMD could take care of. And that's the destabilizing aspect of this, it encourages the holder of the ABM system to go first in a nuclear exchange. Because no one cares if 12 out of 400 missiles are shot down, but they do if 12 out of 12 missiles are shot down.
It then encourages the opponent to make more survivable nuclear delivery systems. Which is exactly what we see from Russia and China: hypersonic glide vehicles, fractional orbital bombardment systems (basically sending the ICBM all the way around the planet so it strikes at the US from the south instead of the north and away from where GMD is deployed), crazy stuff like nuclear-powered cruise missiles and the Poseidon bomb. It encourages further development of nuclear weapons, meaning creating an arms race.
In short, I don't think the ABM systems help us very much in the nuclear war scenario (conventional short-ranged and theater ballistic missiles are a different story).