Yes. MAD assumed that, even if one side launched everything and hit all it could, the other side could launch the remaining stuff and devastate the other side j

Yes. MAD assumed that, even if one side launched everything and hit all it could, the other side could launch the remaining stuff and devastate the other side just as much. First strike capability requires a time pressure that isn't as intense in MAD. For example, Russia's Dead Hand system was designed with the philosophy such that, even if America struck first, there's still enough leftover to post-mortem launch the counter-destruction. That no longer applies, so now there's tons of immediate time pressure to determine if an early-warning alert is a true or false positive.