Not going to get involved in an emotional discussion about whether or not it should have been done. People on both sides ignore what really happened to focus on what they want to be true. The truth is somewhere in between.

As for the ability to build a third bomb, we simply didn't have it. Hansford was barely able to produce enough enriched material for 2 bombs in the time they were needed. The enrichment plant was no where near able to make enough for three at the time. The enrichment takes a lot of uranium. People got rich prospecting for uranium in the late 1940's and early 1950's. My father, a geophysicist, did some uranium prospecting on the side while working on his thesis in Colorado in the mid-1950's. I grew up in the 1960's playing with one of his Geiger counters. But in 1945, we didn't have enough enriched uranium available to make more than the two we did make.