MAD is not military doctrine and never has been. It's a philosophical concept that arose in the mid 1960s and gained column-inches in the press because it had a cool and ironic name. Even McNamara rejected it.

USA, China and Russia all plan to fight and win wars, not go out in a blaze with the other guy. And that includes 'nuclear warfighting' which involves the ability to command and control nuclear exchanges and come out the other side victorious.