In a global thermonuclear war, its not just whether the warhead works (and QA has always been poor) but whether it can even reach its target with other nukes going off everywhere.

Daniel Ellsberg wrote on the topic at some length -

https://cloudflare-ipfs.com/ipfs/bafykbzaceda52mlhlv2o7glq6jijquubugbtfdtmaet6wemrelqno4dkvzll2?filename=Daniel%20Ellsberg%20-%20The%20Doomsday%20Machine_%20Confessions%20of%20a%20Nuclear%20War%20Planner-Bloomsbury%20USA%20%282017%29.epub

US doctrine attempted to make up for this with massive overkill of priority targets.