This is highly disputable. To the extent that it was true during the Cold War, it certainly isn't true post 9/11. The middle east is neither stable nor secure, and Russia has managed to start a deniable proxy war with the west by destabilising Ukraine and Syria resulting in a huge number of refugees.

Meanwhile US anti-drug and anti-communist efforts have left much of south America plagued with violence and recovering from dictatorships.

The thing that is holding the world together is cross-border trade. Both sides in the Ukraine are dependent on keeping the pipeline open, so they've not blown it up. China depends on exporting to the US. I'm not too worried about the Russians nuking London because half of it belongs to Russian oligarchs.