With the success of the Trinity test some of the scientists wanted to strip the thin man and make it into eight fat boys. The fat boy trigger was necessary for the plutonium bomb because the time constants associated with plutonium fusion meant it would tear itself apart before most of the fuel fissioned in a thin man configuration. The fat boy was a more efficient trigger but the thin man was such a simple design they felt their was no need to test it.
The military felt the urgency of delivering a blow was more important than having more weapons later. Their calculations were correct. Two bombs sufficed.
I have always wondered if they had more in case they needed them.