Use of nuclear weapons already guarantees mutual annihilation. I'm pretty sure the US government isn't trying to scare dictators with alien activity - I doubt anyone would change policy without a real alien coming and talking to us.
My point is: if you do a good enough job pretending that an alien has already come and gave us a stern warning, you can potentially influence your adversary's thinking.
That's a weird thing to say.
When was the last time we used them, during a war?
Back before any other power had them. Literally the US was the only country with those bombs. That's obviously not mutually assured anything.
Now, almost everyone has at least one, and the US and Russia have many more.