I think the source is lacking larger context. For example, postwar reconstruction in Europe ushered in an unprecedented age of European states not going to war

I think the source is lacking larger context. For example, postwar reconstruction in Europe ushered in an unprecedented age of European states not going to war with each other all the time. So if you measure absolute numbers of war deaths declining, you can't attribute them directly to nuclear weapons. Also, advances in medicine have significantly reduced the number of deaths in war. It's worth noting that in the American civil war, the vast majority of deaths on both sides were attributed to non-combat disease. So maybe you have a point, but I doubt that it's as simple as more nukes = less deaths.