I agree with you in that decisions like this are always the outcome of multiple forces pushing different ways. But I would lean more to thinking it would have been very difficult for Trueman to have not ordered the use of the bombs.
It would have been electoral suicide because of the extra US casualties.
It would probably have led to the partition of Japan as well as Korea, leading to problems for the US in the post-war world. Although the Iron Curtain didn't descend till a few years later, by 1945, the USSR was already being very possessive about countries in Eastern Europe. Trueman was more aware of the dangers posed by the USSR that Roosevelt had been.
Just because a country had been defeated, it doesn't mean the government will surrender. Nazi Germany was effectively defeated with Bagration and the breakout from Normandy in 1944 but their government fought on to the bitter end. (In a way, the V1 and V2 missile programs did benefit Germany because they drained off resources which would otherwise have prolonged the war and allowed the use of the atom bomb on Berlin.)
And rushing to finish a war to minimise the influence of one party on the peace negotiations did have a precedent. It was what the French and British did at the end of WW1 to prevent the US from dominating the peace process. (But that didn't turn out very well.)
I think things like this would have been in Trueman's mind when he made the descision.