It's important to note that the nuclear program started as a race against the Nazis. Japan had no nuclear program during the war. Once the Nazis surrendered, there should have been no need to continue the development of the bomb. It was developed and then ultimately used on civilians, not once, but twice.
And if Japan hadn't surrendered, it would have been used up to a dozen times.
The third bomb, and the others that may have followed, were a definitive part of the American strategy to end World War II. Although hopeful that nuclear weapons might end the war, American officials—from President Truman to his commanding officers—did not expect the war to end right away. Signs indicated that more atomic weapons were necessary, and U.S. leaders were rapidly moving to order more atomic strikes. Had the war continued, more atomic bombs would very likely have been used.
While that is true, as declassified documents show, it's important to note they didn't have that many more bombs ready at the moment (IIRC they did have a third one ready to be dropped) but they were being manufactured as quickly as they could, so the war would have to last a while for all of them to be used. But they planned to, which is a little scary
The nuclear bombs were hardly more cruel than any other part of WW2. Nukes killed a comparatively low number of people. Per unit, nukes are scary, but it was just a drop in the bucket.
The Japanese did have a nuclear program that made little progress and was unlikely to be a threat.
Ultimately your use of the word "should" implies that Japan would not have fought out the battle on the main land. Killing civils is bad, saving millions of lives is good.
On that note, I highly recommend the book Racing the Enemy by Hasegawa Tsuyoshi. It's a very in depth look at the weeks before the surrender from inside the emperor's cabinet.