"That never been the case, even at the peak arsenal levels. USSR, and USA bombing each other into the iron age? Yes, but not much more."
I was also surprised to learn that directly killing every person in a country with nukes is impossible.
However, Nuclear Winter might finish off most or all survivors - models predict massive fires triggered by nuclear war, soot in the upper atmosphere leading to major temperature drops and widespread famine. Surviving that after all infrastructure and industry has been obliterated, and with widespread radioactive fallout...
Suffice to say that I agree with OP's overall point, we have the doomsday machine.