The purpose of a retaliatory posture is the foundation of MAD. If the posture, instead, is: We'll just rollover and die, then (the theory goes) there's reduced reason for others to avoid a first strike.
Yeah, I understand the reasoning of MAD, but on like a thinking individual level... when you get the order and are under the impression that this is a second strike, why hit the button? MAD clearly didn't work at that point, so why fire? On the off chance that it was a small first strike and this is a limited second strike? I, at least, would rather run the risk of upsetting the doctrine than run the risk of destroying all of humanity.
Perhaps there are 2 kinds of people: those who think the way you're describing, and those who would hit the button to retaliate. I wonder if the people who end up sitting in the missile silo are selected for the job by asking them how they would respond.
Did you by any chance read the _Three Body Problem_ novels? It is partly about this problem, but I won't describe the details because of spoilers. Highly recommended.