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Hiroshima and Nagasaki had 60 times as many deaths and many more with lasting injuries including radiation sickness, and rather than being shoved down everyone's throats by the media and politicians as a justification to start a bunch of pointless wars that got a bunch of people killed, they were instead used as a reason to end a stupid pointless war that got a bunch of people killed. There's good reasons to mock 9/11, but not the atomic bombings.

More generally though Americans tend to be more irreverent, and imo a lot of that has to do with religion. Most Japanese people aren't religious at all, and their religions don't often intersect with the political sphere - it's almost unimaginable if all you've known is the US. In the US, mocking certain topics is a way of establishing which group you belong to, and there's many different groups in the US who all hate each other and are constantly making fun of each other.