(this originated as a comment of mine in reply to
tepintzin to an earlier post of mine)
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What I think would happen without the United States keeping the peace is that, suddenly, in many regions of the world aggressor-states would find themselves much stronger than potential victims, and before regional organizations could create a collective-security defense, many small to medium-sized wars would begin. If things went badly in any area of the world, a successful Regional Power aggressor-state might conquer enough of its region to become a Great Power, and from that platform of power lay its designs against other regions.
Absent any global peacekeeping collective-security organization (and the UN is rather clearly no longer able to fill the role), the aggressor-state Great Power would then be able to launch a medium to large-scale war, with the intent of becoming a Superpower, and eventually dominating the world. This would, of course, then lead to a World War.
Such a collective-security organization would have to be centered on a Great Power -- which one or ones do you think would step forward to assume the role if America didn't? And which ones could be trusted, in that role, to behave as benevolently as did America?
There is a very good chance that our attempted withdrawal from the world would simply lead to our forced participation in World War III, a decade or two after our retreat.