The U.N. isn't a country....although some liken it to one....Those groups of nations you have mentioned aren't doing too much without the U.S.A. either, are they?
You can call it what you want..."gamble", "loser of an idea"...I happen to think that would be the quickest way to see the end of the U.N.
Will it happen? I doubt it...They/We will probably putz around doing it "your way"...and it will be more of the same, same as it ever was.
FWIW-
That's a popular *theory*, but it's no sure thing.
Consider, we *did* take the U.S. money out of the Kyoto Global Warming treaty, and yet, that coalition of nations still lumbers on with that treaty. Ditto for the U.S. pulling out of the International Criminal Court; that court still exists...merely funded by Europe instead of the U.S.
So here's my reply to you: Kill the UN first, and *then* the U.S. can give up its UN veto.
But I see no reason to first surrender that veto in the *hope* that the UN will then die without us.