But MAD means you can't use them. It might save you from an all out killbot invasion but it doesn't stop asymmetric warfare or being cutoff from the rest of the world.

Unless the AGI is able to develop effective defences to intercept an incoming nuclear attack.

MAD is a belief system. It doesn't matter whether AI can effectively stop the retaliation, it is enough that people making the decisions believed that it can (are we there already?).