High ground has little meaning in the world of ICBMs. It's all about (theoretically) firing them fast enough to kill your enemy before they can counterstrike.
The moon is an average of 380,000 km from the earth. The LGM-30 has a maximum speed (which it only reaches at the terminal phase of flight) of 24,100 km/h. Even if we theorize that without having to break gravity that the missile is 5 times as fast (pulling that number out of the air based on the fact that escape velocity from the moon is roughly 1/5 of earth), you're still looking at over 3 hours to get close to the earth.
The LGM-30, on the other hand, starts deploying the payload towards the target about five minutes after launch.
If there _had_ to be nuclear war, the powers that be would be *delighted* to get a three hour headstart for the bunkers (and time to properly target incoming missiles with defensive measures).
Lunar missiles would also be subject to ridiculously high maintenance costs, damage from the hazards of space, and would either have to have human operators living there (again, incredibly expensive) or you'd have to trust remote control of launches.