There were multiple reasons that the people behind the atomic bombings had for wanting to drop them. (And almost no reasons not to.) The primary ones were to terrorize the Japanese, with the hope that this would make them more amenable to surrender. This is very clear from the documents at the time — that they hoped the psychological impact from destroying cities instantly with a new weapon would make the Japanese more favorable to unconditional surrender demands.

There were some, notably Secretary of State Byrnes, who recorded their hope that the US possession of the atomic bomb would also aid in their negotiations and postwar status vis-a-vis the Soviet Union. That was an additional "benefit" to using the bomb.

There were also those, notably among the scientists, who hoped that a horrific demonstration of this new weapon would lead to a universal ban on them in the future, or at the very least to their future non-use.

There is a lot of scholarship on what exactly resulted in the Japanese surrender, but that is a different issue than the motivations of the Americans who were in charge of dropping the bomb. One should not conflate the two because these are unrelated (the Japanese had their own reasons for doing things disconnected with American motivations).

Hasegawa's Racing the Enemy does a good job of explicating the various motivations for dropping the bomb, especially around the time of the Potsdam conference. It also does a good job in trying to tease out the complicated events that brought about the end of the war. It is all more complicated than your post indicates.