I don't think the casualty estimates of an invasion were too high. In fact some of the estimates coming from MacArthur's crony staff boys were ridiculously optimistic. The Japanese had stashed a bunch of Kamikaze aircraft and suicide midget subs etc. just for the projected invasion. In addition they had pretty much figured out the only good invasion points on Kyushu for the initial phase of the invasion, and had moved their troops accordingly. The losses to the Allied naval and land forces during the invasion would have been high, to say the least. And this is before the troops, once lodged ashore, had begun the slog up the island to their objective (about a third of the way up the island). Meanwhile, the strategic bombing campaign would have continued, taking FSM knows how many civilian lives.
And once the objectives of the first phase were achieved, we see it all done again the next year on the Tokyo plain during the second phase (assuming the Emperor hadn't come to his senses as he did in the real timeline).
Nuking them was a tough decision, and one I also am glad I didn't have to make, but I really think it was a no brainer given the situation, when such a weapon was available.
Thing that people seem to not understand is the enormous magnitude of the task.
The D-Day invasions were landings into France, an occupied country. German soldiers were the only enemy to be fought, the local inhabitants were not fighting on the German side. Also, the allies pulled off a number of cunning deceptions...Operations Fortitude, Graffham, Ironside, Zeppelin, Copperhead and Mincemeat in the lead up to D-Day, and Operations Taxable, Glimmer and Big Drum on the Day of the invasion. These operations fooled the Germans into believing the targets of the invasion were elsewhere or happening at different times than the real invasion. They were able to get away with these deceptions largely because of the short trip across the English channel under cover of darkness. Then, there was mainland Britain not far away for supplies and materiel.
It was a very different situation in Japan. Deceptions would have been much more difficult to pull off, as the Japanese would see them coming for miles. Also, the Japanese public believed that Emperor Shōwa was a descendant of Amaterasu the sun goddess, devine, and a living god, and therefore, all powerful. The landing armies would have been fighting not only the IJA, but the entire population (72 million in 1945) armed with anything they could find to use as a weapon. Establishing a beachhead after landing would have been a monumental task that could very easily have gone terribly wrong, and nowhere to go if it failed. Casualty numbers could have been horrendous.
As others have said, bombing Hiroshima was probably the right decision (I'm not sure that Nagasaki was necessary) but I would not want that decision making responsibility to fall on me. I think if you asked any of the Allied soldiers whose job it would have been to invade Japan, if it was the right decision, you will pretty much get a resounding "yes"!
