If you think the world is stable as a result of the US, you should think again. It is exactly the contrary. The US itself is involved in wars since basically its foundation. The reason you say this is because you probably live in the US or one of its rich close alies. Everyone else will tell you that life under US hegemony means constant wars, coups, and political instability.
Could you give some examples? The US has certainly abused its power (notoriously, in the 60s and 70s at the height of the Cold War), but "constant" appears to be stretching historical fact to fit a narrative.
Are you forgetting that the US has been actively involved in non-stop wars around the world for the last 20 years? And before these wars started, it was doing "special operations" in eastern Europe, parts of Asia and Africa? And in Latin America it never really stoped its coups, military dictatorships and the such, especially in central America. And then of course there was the "cold" war and all the crimes in South Asia...
Look at the hundred years before that. Everyone was fighting, all the time, not just one country with roughly one skirmish (by historical standards) at any single point.
