"Stone and Kuznick noted that such an outcome would have dramatically changed the American landscape after World War II. Because Wallace never would have dropped the bomb, the U.S. relationship with the Soviet Union would have been maintained and the arms race and the Cold War would never have begun." https://yaledailynews.com/blog/2014/10/16/oliver-stone-discusses-atomic-bomb/ Stone of course is no historian but Kuznick is (I'm not saying he's a good historian..). And given their sales, it is reasonable to assume that many people agree with them.
Anyway, I have seen other people here say it so maybe I should just have said "Many people here assume..."
"And given their sales, it is reasonable to assume that many people agree with them"
Actually it's Stone's name that pushes Kuznick's theories but neither is widely supported in historic circles. And there's a reason for that, if their characterization of Wallace as an "active opponent of the bomb" isn't enough of a hint here. Put simply it was pretty clear that despite what had already been done to Japan the military was in no mood to bargin in good faith and historically the attempted 'imprisionment' of the Emperor showed this to be true.
There's an semi-common assumption that Wallace was a closet Communist and "weak" liberal semi-pacifist which isn't what his history or writtings show. Likely he WOULD have used the bombs as most people at the time, (imporatnt to keep context) felt that unlike Germany, Japan was not going to surrender the home island to occupation and nothing less was acceptable to the allies. Further he was aware of Soviet aims in Europe and Asia and despite some understanding of the circumstances, (the USSR wanted 'buffer' room to avoid yet another invasion by supposed-allies or real enimes which given the history behind it was actually understandable if not being acceptable in reality) was worried about post-war Soviet intentions as anyone else.
As noted Wallace was at least familar with and somewhat understood the nature of what was expecte of Atomic weapons whereas Truman had neither the inclination nor interest other than 'big-boom'. (And was rather proud of the fact mind you) Wallace had at least a passing knowledge of both the implications and usage of atomic weapons to a larger degree than Truman and more specifically, (a point I'll get to in a moment) understood that it was not a "cheap" way to assure US post-war dominance. It was, while not "simply", another weapon of war albeit much more powerful than anything humans had previously had it was not in and of itself a "war-winning" wonder weapon which is the opposite of what Truman believed.
We know now that it was the Russian attack and fear of an allied supported invasion of the home islands that forced the Japanese surrender. That the bombs were simply a further bit of evidence that any further resistance was doomed and would only make Japans post-war fater worse with no possible return. Despite this the military STILL tried to avoid surrender. Wallace was no more a fan of an actual invasion of the home islands than FDR was and for the same reasons really. So it's very unlikely he would NOT have used the bombs and more had it become neccessary. Similarly Wallace agreed with FDR on limiting Soviet post-war influance in Europe and Asia, (and here again Stone/Kuznick's hypothisis doesn't match the reality of the situation) and also agreed that enforcement of the post-war divisions would be required.
Now the question around that is how would that have differed from Truman's immediate and drastic drawdowns and efforts to expedite American withdrawel both militarily and otherwise from Europe and Asia in the immedate post-war. Truman's post-war budget and defense policy was driven by his belief that the Atomic bomb coupled with USAF long range bombers made most if not all the then 'current' military obsolete and therefore his post-war defense budget spending and policy pretty much demanded an immediate and full withdrawal of US military forces from just about everywhere as soon as possible and demobilization of forces. This despite the allied agreements for the bulk of the occupation forces being US in nature. My read is while Wallace would not be popular for NOT immediatly drawing down the military as Truman did a more gradual draw down and less dependence on the "atomic" option would have had a pretty profound effect on Soviet policy and not in the "no-Cold-War" sort of way.
Randy