I don't think it is that funny, but I don't think it is in bad taste either.

Hiroshma was a tragedy, but one of which I don't know it could be avoided.
Still, laughing with tragedy is a human way to deal with it. ER doctors laugh with what they deal with, as do lawyers, undertakers, ...
It is simply a way of dealing with it.
The same goes for the Mohammed cartoon.

As for the bombings...
60 years later it is easy to take weeks pouring over information, and then deciding what the people of the day had only days for, with unreliable info to base their decision on.

The one good thing that flowed from the bombings of Hirsohima and Nagasaki -which were terribly inefficient, as far as nukes go- is that everyone became so scared of MAD that noone ever depolyed the real bad boys, like the megaton hydrogen bombs.

I also think that the pilots didn't know what they were going to drop.
They would've known it was out of the ordinary, but with the 'need to know' in the military, they would not have known what they were going to cause.