I have never read this and cannot believe it, it would be contrary to US constitutional principles to wipe out 2 billion innocent people if the launch was done say by a North Korean submarine, but please post some link. In the case of decapitation, strike time is crucial, in as little as 30 minutes a SLBM (MIRV) could strike the Pentagon and Washington DC simultaneously. I know US has a protocol to activate the Minuteman in this very case when the President and the Secretary of defence are dead but I cannot believe they would launch everywhere, it is no more a cowboy nation and especially when it comes to nuking everything is programmed in the smallest details otherwise we would have had some accident already. Part of the decision-making process will be managed by AI in the very next years but US will remain
a country ruled by law, everything in US including nuclear war must be under the umbrella of the constitution, the pentagon chief reminded (recently in the election aftermath ) the US population to upheld constitutional values.
This is all purely conjecture posed by academics. There is no book on how to react when an unknown origin SLBM pops your capital city. Imagine that... no one nation has published their strategic and tactical response manuals.
I've explained the reasoning and cannot be bothered wasting hours tracking down the dialogue and written conjecture exploring this topic... in a very informal way. You must only think about it rather than expect official paperwork on the topic.
Rest assured, the US would not respond well if there is a ICBM/SLBM coming its way, let alone detonating a KT/MT warhead in Washington DC. Russia and China would be shitting themselves if this ever happened. There is no way Russia or China would shoot just one or a few missiles if it means business in a decapitation strike. Same with everyone else (if they have the material like the three main nuclear powers). I don't expect the US to assume a sole or limited strike on its cities to be the work of North Korea. Your hypothetical scenario is too far removed from reality to consider.
The principle of extended MAD makes sense. It moves the nuclear escalation action onto a higher ladder, making it a safer world. It's not about 2 billion lives or 7 billion. No hollywood rogue state or terror group is likely going to get SLBMs and North Korea wouldn't be doing this for no reason out of the blue. That's not how real life works.
If the US is hit and throughly damaged by ICBM or SLBMs and there is no way to tell who or where? they will very likely respond with massive attacks on Russia and China. If it's a singular missile that somehow escaped all interception and early warning, they might assess. Again there is no handbook publicly available. But rest assured that if their destruction is comprehensive, they will assume it is Russia and/or China. Even if they know it isn't. Do you really think there is 0 chance of US strike on Russia and China when it is condemned to that fate? The unspoken acknowledgement is that any nuclear power being struck down comprehensively (assumed) is going to make life hell for everyone else. This on principle makes it everyone else's responsibility to keep them alive and not reach nuclear level escalation.