Post #143 highlights why you are wrong in your interpretation.
The pope seeks a world authority that has the teeth to enforce among the nations what he is proposing. There is no doubt, that is, if you trust the pope’s own words, straight from the Vatican.
Exactly what is the Pope proposing? That is, what does he see the UN being? Like it is today? From the paragraph you cited, it seems clear he is probably as dissatisfied with the UN (as it exists today) as we are.
This all comes back to the concept of "poverty of spirit", IMO. We must not be so entrenched in our (I believe justified) hatred of the UN as it operates today, that we will automatically reject any idea of some kind of governing body for the entire world.
Again, the tenor of the Encyclical seems to be a single proposal to people to govern themselves under Christian principles, i.e., the American experiment. So, re-reading the paragraph you cited in this light, to me, it seems that the Pope is saying that the UN needs to be reformed, reformed to abide by its original intent (or charter).
Put another way, if we put aside any paranoia inspired by pre-tribulational "rapture" eschatology that may plague us (not that it does you, but it clearly motivates some), if we imagine a governing body that is exactly modeled after the United States' (ideal) government, who would object to it?
Why object to it? Let me make my hypothetical scenario clear: What if the UN (or some other world body by some other name) were modified/created and it behaved exactly as the US Federal government was supposed to behave? (Limited intrusion into people's lives, limited taxes, both financial and physical, freedom of religion, speech, assmembly guaranteed, etc) Why should we object to that? Simply because it's a "world government"? To me that would be putting patriotism over Christian principle, quite frankly, not to mention, again, letting paranoia generated via a (relatively new) eschatological belief make our decisions for us, instead of engaging our own God given freedom in true "poverty of spirit".
I think again it's important to note that the Pope isn't proposing any specific way this world body would behave other than to say it should be as the UN was supposed to be: a body that would protect the rights of all people.
Isn't it interesting that the main reason the UN is such a travesty today is not because it adheres to its original charter, but precisely because it does not adhere to its original intent to protect the individual rights of all?
So, again, without expressly saying that I agree with what he is proposing here (without further reflection and careful examination), I can't say I find the idea too objectionable. In fact, right now, the only reason I can see why I would find it objectionable is if I automatically, and without hesitation, always rejected the simple notion of globalization. As I stated previously, to react in such an "instinctive" way to the concept (or indeed to any concept) is to not truly be "poor in spirit" (as the Beatitudes say we should be).
We must have a reason, based in reason, to reject a proposal. We can't simply reject an idea simply because we were taught to always reject it. That's not the way "reason" works; quite frankly that's how animals behave.