Yes, they are truly horrific weapons. However, people walk around Nagasaki, White Sands, and various Pacific atolls and live. People are able to live near Fukushima Japan and there are workers near Chernobly in the Ukraine.
Radiation can kill. However, it can be diluted to the point that life can go on. Fear of nuclear contamination, and the economic disaster to remove all radiation is the real threat. Fire hosing down the contamination and diluting it and going on with our lives would be not that big a deal.
Yes; the greatest destruction of a nuke comes from the heat and pressure wave, not the ionizing radiation.
The difference between what hit Hiroshima and Nagasaki and what is around today is a matter of scale. And of course, there is that nuclear winter hypothesis with the 100-city-firestorm thingy.