The US states that that is an option it make take. It does indeed make no sense, that's why it's called Mutually Assured Destruction, and it works.

If it didn't take this position, it then makes nuclear war more likely. It is actually a logical position to take since you can assume tit for tat nuclear strikes are a given, so there is no advantage to drawing it out.

It may of course not take the option, but the opponent doesn't know what it will do. It's all a part of the nuclear force being a deterrent to war.