One of the reasons often used to justify the use of nuclear weapons is that the alternative strategy, firebombing and invasion of Japan, would have caused much more death and destruction for both Americans and the Japanese. But I wonder, why was an invasion the necessary alternative?
As I understand, Japan was running low on resources such as oil, rubber, and steel, even from the beginning of the war. If the invasion of the homeland looked so costly for both sides, why was it deemed necessary?
I'm not aware of any allies Japan could have counted on to supply it; why not maintain a blockade and wait them out? It seems that that would have cost less in terms of American casualties.