> Both peace settlements following the wars were widely criticized as unstable and unlikely to last, and they didn't.
Do you mean that "the" post-WWII peace settlement didn't last? It seems to have worked very well.
> It wasn’t America's principles that made it the world leader at the time—it was the fact that, unlike other major powers, it emerged from the world wars largely unscathed.
That certainly played a big role. Also, American principles that created a post-war order based on univeral human rights, the rule of law, and free-market capitalism (including free trade). Those principles led to treatment of the losing powers in that image, rather than in retribution, cruelty or oppression (compare to the USSR in Eastern Europe). In fact, Japan surrendered when they did mainly in order to surrender to the US and not to the USSR - those principles had very significant effects. They also led to the Marshall Plan in Europe.
The principles and the resulting actions created 'soft power' which may be unmatched in history. The general alliance with European powers has lasted over 80 years; the NATO military alliance, of mutual self-defense, has lasted almost as long - has there been anything like it?
People around the world fought and struggled for the vision of American freedom. I've spoken to people from different countries who, even in the first Trump administration, still had the American dream; they still saw the 'city on the hill'.
Beyond a doubt, the US also has done plenty of awful things. But what has distingiushed it, beyond every great power in history, are those principles.