I can’t see why any powerful nation would join the thing if they thought for a second it might turn on them.
There's the five permanent UNSC members, all of whom would realize "Hey! I can just veto any potential attack on me!" so why would they care? A few of the Axis nations can be bullied in because they're not in much of a position to actually do much. Perhaps some smaller European nations would still have the memory of Hitler at hand, and join the UN thinking of it as better protection (think of how much Belgium would've appreciated an international police force saying no to Germany 1938, for example). The Warsaw Pact would be bullied in (USSR wants as many votes as possible in the UNGC), as would the European empires (for similar reasons). At this point, you have a pretty sizable percentage of world nations and total global power. Outside of that, what's stopping the UN from intervening in a non-UN nation? Not joining the UN doesn't necessarily mean the UN will ignore human rights violations.
Keep in mind, one thing FDR (or Truman?) was considering with the UN was that only the five UNSC members would be able to legally hold militaries. Merely having the UN able to overstep national boundaries is actually less radical than some of OTL's ideas.
Britain would be the biggest block to this, I think, and the reason why it wouldn't happen in the end.
