The AD - Assured Destruction - part works just fine. Irrational actors don't assemble world ending arsenals (after all if you think you should rush to your death, why not launch when you have 1, given that you're most likely in a "use it or lose it" situation).

Even in your cited example - the people who do this sort of thing attack those who can't fight back. They are never in any danger of being immediately shot dead after.

While yes suicide bombers exist, this is more a question of arms proliferation and control then an indictment of the ineffectiveness of MAD or the general strategic reality of nuclear weapons. And the situations under which non-state actors have them are still a policing rather then political concern - North Korea or Iran leaking a bomb to another entity that then detonates it is the surest possible way that both those states will be dismantled by NATO, since MAD does apply there: proof that you represent an uncontrolled risk of nuclear attack invites conventional or nuclear annihilation, regardless of the mechanism. Civilian casualties go out the window when you have already suffered some.