the irradiated? lots of people survived in Hiroshima and Nagasaki and had to deal with cancer and other radiation related health issues after.
That was 2 cities, and there was still the entirety of global civilization still functioning beyond them, providing a means of recovery and a hope for the future.
Global civilization wasn't really still functioning this was the end of WWII. Europe was in shambles and the more industrialized parts having been carpet bombed, the Germans Italians British and French had lost/were losing their empires. China had just been broken first by civil war then by the Japanese. Pretty much the only industrialized nation to come out not broken was the US.
The people who survive, usually. It's obviously scale dependent, but I can't imagine not wanting this around just in case. Many humans will survive initially and we will need everyone we can to try and find a way to survive.