I'm not clear which of my points you disagree with.
Also, there were three Axis Powers in WW2, and two of them had fought against Germany in WW1. It's overly simplistic to say that post-war suffering in Germany was the sole cause of WW2--especially as there were terrible sanctions after that war as well, but Germany has not gone to war again.
Europe was all about Germany being stuck between a rock (the post-war sanctions) and a hard place (the threat of the communist revolution that Germany implanted to defeat the Czar to the money men in Germany). Italy was a sideshow.
The difference in the post-WW2 era, and the reason we didn't have WW3 in 1960 is simple. The US emerged triumphant and essentially occupied or otherwise controlled all of the powers, save China and the Soviet Union. As the US loosened control, mutually assured destruction made WW1/WW2 style "total war" too costly.
I wouldn't be surprised if future historians view 1914-1989 as one war.