But why "imperative"? That implies that there was absolutely no other choice.
A starvation blockade and conventional bombing would have been options --followed by a demonstration of our wonder weapon and then perhaps a negotiated peace, or perhaps unconditional surrender.
I'm not saying that we should have done that -- politically it may have been an untenable position, and we could be blockading and bombing them still today -- but it was alternative, at least in theory.
No doubt they were options, but they came after invasion. The invasion was the selected course of action, the bombs were an alternative to the selected course of action because if they worked it was thought they would achieve the desired result. Blockade and conventional bombing never met the strategic objectives, which is why they weren't selected.
I realize I was deliberate in choosing imperative, because I advocate for those who are long dead and/or are passing away. They were past the point of considering options for dealing with this crisis.
You do make me think I should work on the narrative to emphasize the increased fragility of support for the war based on the huge increase in casualties for the 12-15 months leading up to August 1945. The country really didn’t feel the human cost the first two and a half years of involvement. But then Europe beginning June of 1944 and Okinawa in spring of 1945 hit this country hard. I remember the story told by one man who was too young to serve, but as an adolescent delivered telegrams part-time for the local Western Union office. He eventually quit, because every day he had to deliver the death notices and people began looking at him with some combination of anxiety and hatred.