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Yes, I agree with you that the "peace" mostly applies to those in the fold, and the only people who enjoyed a real, enduring peace for the whole time are the middle and upper classes of the very core of the empire. Personally, I would suggest that much of NATO (but not all of it at all times) has had relative peace during this time. The borders of empires have always had belligerents that need "putting down" from the perspective of the empire, which means small proxy wars. However, the "peace" usually refers to wars between nation-states.

Much of Europe's economic policy benefits from the huge subisdy that the US covers them with its guns - a drain of 6-10% of GDP may otherwise apply to NATO countries that find themselves up against Putin (and in a hypothetical world - maybe against each other). The Marshall Plan is also a relatively visible indication of how intertwined Europe's post-WWII growth was done with America's involvement, and when you look at US foreign aid ("imperial economic stimulus"), a lot of it today goes to poorer European nations. I agree with you that the EU (post-iron-curtain project) has been, as you suggest, a solely European initiative driven more by European solidarity than US guns. However, it exists in the world of the petrodollar (not any more) and with the quiet reassurance that many of the leading nations in the EU are NATO members. As we have seen with Ukraine, sometimes that NATO membership matters.

Empires are always a lot looser than we think - the Roman empire was a great example of this, where the nation-state of Rome (in the modern idea) didn't extend beyond the Alps until the Caracalla years, where Roman citizenship was truly extended to the provinces (note: after the end of the pax Romana). Egypt and the levant were basically completely autonomous, much like the EU is today.