Sure, it would be nice if such a thing existed and at the same time, proposed only laws that really were for the common good as the church defines it and always followed those laws and every nation always followed those laws but it will never happen and to give such authority to some sort of international body to force compliance is dangerous because at some point, it will fail to live up to it's ideal.
That is pretty much the argument anarchists use in urging that any
government is a bad idea.
I also don't understand how this fits into the Church's support for the sovereignty of nations.
During the Middle Ages each kingdom (and at least two republics I can think of) was sovereign unto itself; yet throughout Christendom universal laws were known and (largely) observed. There's no contradiction between the two.
...the prospect of what he proposes actually frightens me.
Actually, I find a world of law and order more appealing than a world of brute might and raw power.