I never got that logic—the US has been in armed conflict in various forms since the end of WWII, whether directly or through the CIA. It seems more like nukes enable violence from my perspective.
Europe, for sure is a lot less violent, as for the rest of the world? I won't believe that on face value; south America specifically got more violent, and I suspect everywhere else is a wash (or is not attributable to American force projection). I attribute the peace in Europe to the EU rather than pax Americana.
Overall violent death is down on planet Earth drastically over time.
But I’m with you, on balance wmds are terrible things. One use of them could outweigh all the violence they prevented.