As is often the case, this is technically true but leaves a planet-sized portion of the story untold.
Undeniably, large groups of people have enjoyed "unprecedented peace and prosperity" while many others, even inside the democratic Western states, have been compelled to live impoverished, violence vexed lives (with the violence sometimes coming from local factors such as criminals and police, and other times coming from the wars they're fighting on behalf of the state...such as Vietnam and Iraq).
It's important to understand the importance of Europe and Asia's 1930s/40s era devastation and the introduction of nuclear weapons (a category of device few people properly understand) when evaluating the lack of large, set piece warfare and the creation of the so-called Pax Americana.
The US could more easily craft a global order to its liking -- and suited for its
economic and strategic needs -- with former adversaries and current allies lying
prostrate before Washington's feet; exhausted by years of super mechanized war.
The arrival of nuclear weapons raised the stakes in unexampled ways of embarking on large-scale aggression against fully industrialized, nuclear armed states -- contributing to a kind of selective peace, one in which WW2 size conflict was replaced by small scale proxy and asymmetrical wars (with important exceptions outside of the Euro/American axis such as the Iran-Iraq war...a conflict between two non-nuclear rivals and, therefore, in some aspects an example of the sort of pre-nuclear age conflicts Europe experienced).
.d.
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