In the case of a nuclear attack, most of the nuclear “chain of command” would be targeted and, realistically, many would not survive. The continuity of government plan for a nuclear attack isn’t designed to get all the influential muckety mucks out of the frying pan, it is to attempt to get the bare minimum of decision makers to secure facilities like Site-R or onto Doomsday Planes so they can wage an all-out nuclear retaliatory war. Very very few people would make it out of DC, and even getting anyone Sec Def or above out would be a very close thing.

The point is that for deterrence to work, it has to be credible. If Russia thought it could “kill” the US government so that no one would be able to effectively order a counterattack (either because they are dead or because they can’t communicate orders to actual nuclear forces), would they do it?