Do you believe any country has enough conventional ordinance to end human life on the entire planet? You must know more about this than me, I've never heard of something like this.
https://en.wikipedia.org/wiki/Cobalt_bomb
>After one half-life of 5.27 years, only half of the cobalt-60 will have decayed, and the dose rate in the affected area would be 5 Sv/hour. At this dose rate, a person exposed to the radiation would receive a lethal dose in 1 hour.
>After 10 half-lives (about 53 years), the dose rate would have decayed to around 10 mSv/hour. At this point, a healthy person could spend up to 4 days exposed to the fallout with no immediate effects.
People can't stay in bunkers for 20 years at a time, just to emerge into a radiated hellscape.