Exactly!
The intangible disruptions of a human society will indirectly cause eventual death due to the nuclear war. Think about it, just the COVID-19 lockdown of a few weeks can cause economy collapsed, people out of jobs, can't paid rent, utilities. A nuclear war will immediate cut off or contaminate essential human necessities, like food, water, shelters, electricity etc., so even without getting harmed by kinetic force, radiation, climate alteration, people still cannot survive long term.