You're overestimating how much damage a few thousand nuclear bombs can do. Even just targeting every big city in the world you'd struggle to kill a billion people directly, though the aftermath may bring the total that high.

> the standard response to a nuclear attack ends human life on the planet.

No, it really does not. Mutually assured destruction - especially with current amount of nuclear weapons, which is an order of magnitude less than at the peak of cold war - means unacceptable level of casualties on both sides, however, even an all out launch-all-nukes NATO vs Russia war wouldn't even touch the regions where majority of human population lives. Sure, it would be an extremely horrific genocidal event, I personally would die, but even reducing population by half (to 1974 level) is nowhere close to "ends human life on the planet".