I'm not sure they would. But as I said, I do think that something on the order of the UN's original charter, which was essentially a meeting-place for discussion and consensus, would be extremely useful in a world with this very peculiar geopolitical alignment.
But the original charter was quickly forgotten in a rush of enthusiasm for world government by a self-proclaimed elite. At some point the emphasis was less on discussion and consensus and more on rule, and I cannot imagine what would have happened had the UN been given possession of all the nuclear weapons in the world or its own independent armed forces, both of which options were at one point more or less seriously discussed.
It is ironic that those who are at present pouring barrels of ink into lamenting that the U.S. is attempting to rule the world seem so insistent on effecting precisely that on behalf of an unelected, unaccountable, and provably corrupt UN. I suppose it's natural enough for a forum full of world leaders to expect to lead the world, and by extension, for a forum full of dictators to expect to be able to dictate. But that was never part of the deal.
As to why we should have a UN at all, there are a dozen cogent reasons for forming it in the first place that still apply. For one, it performs a point for coordinating disparate nations' aid efforts in time of natural disaster. For another, it should (although it does not at the present) constitute a neutral venue for parties in dispute to settle their differences short of war. For a third, it should constitute a means for collective efforts between nations to be coordinated on issues which should properly not fall under the direction of any individual nation - eradicating a disease, for example.
But not rule. And not a dinner table at which all the diners order their hearts' desire and pass the tab repeatedly to the same guy. And not a means for those who desire power to assume it without earning it and without being accountable to those over whom it is exercised.
I like the way you write, and admire your obvious intelligence and earnestness. I also agree with much of what you said. However, I disagree that there is any useful role for "a UN." I hit an absolute brick wall when I saw the phrase "collective efforts." No thanks.