We may just need to agree to disagree on the point of the inspiration of Paul's writings. Both he and Peter both believed that his letters constituted the word of God. But that aside, I don't think Romans 13 is necessarily a statement against anarchism. Could it be that God expects us to submit to state governments that exist to the degree that said government promotes freedom of conscience? That doesn't necessarily mean that any government is God's ultimate intention. Is it also possible that although Paul wrote that, he also believed that the ultimate expression of the kingdom of God on earth would be a society that looks to God as king, not man? It seems this was God's original intention for the people of Israel but they insisted on making a man their king.