Obviously, I hugely admire More as a man of principle, and I completely get where he's coming from with this. However, I don't personally believe the Church should have any "authority" over earthly governments (whether Catholic or Protestant). That said, it should (if it is effective) have spiritual authority over the demonic realms, since Jesus directly gave the Church this authority. That authority remains, with the Church being the "salt of the earth" so to speak, keeping the spiritual evil that manipulates earthly evil in check to a greater or lesser extent (depending on how effectively it is doing that job), until the time of the Antichrist, when God himself ultimately steps in. But that's getting into a huge theological discussion that I daresay shouldn't be held in these forums.
Excellent article by the way. :)