For instance, Hiroshima and Nagasaki were rebuilt without issue after a few months,
Those were both air bursts, which limits that, since less ground and debris is vaporized to be drawn up into the cloud and latter scattered.
Radiation is sorta weird in that you have to have something to be radioactive, radiation isn't its own thing the way something toxic like an oil slick or heavy metals are. So the bomb going off could give all the people not killed outright by the blast wave radiation poisoning, but after that happened, that was it. Nuclear weapons spend most of their energy being a bomb, not a poison.
So Airburts really limit the amount, and spread, of materials that can become radioactive.
Thanks to Hollywood, radioactivity is one of the more misunderstood subjects around, and the general negativity surrounding nuclear weapons in general only serves to reinforce the worst case outlook on things. Combine that with the oil industry wanting to make sure we don't ditch them for nuclear power, and there's a lot of negative coverage of nuclear anything, and not a lot of positive.
Three Mile Island is treated like a nuclear disaster, and its a boogey man for the entire concept, and was a major factor of the death of nuclear power generation in the USA, and yet, the actual damage caused by it was equivalent to flying from New York to LA, and back again, and under 1000th of the yearly dose allowed to US radiation workers, That's right you could hit a Three Mile Island every day for a year and not go over your safety margin. And that's still half the dose ever linked to increased cancer risk. And emergency services are allowed to absorb 5 times that before getting pulled out. We're
very conservative about our radiation safety.
It's something to be treated with respect to be sure, like any other number of potentially dangerous pieces of technology, and safety should be taken seriously, but radiation isn't nearly as dangerous as most people assume, or rather what constitutes a dangerous amount isn't what most people imagine, compounded by the fact that different kinds behave differently and it really gets messy. Alpha radiation for example is potenially quite dangerous, but its ability to penetrate is so feeble you'd have to literally eat it to be at risk. You could use a lump of something that only emitted alpha radiation as a stress ball and it'd be basically harmless.