You have to keep in mind that this was written in the early part of the Cold War, when the ancestors of today's Lew Rockwellians were arguing that Communism was an imaginary threat, and that defending ourselves against it was not worth a dime of public funds.
Actually, Kirk was a follower of Edmund Burke, whose core belief was that traditional values were good not because they were handed to us by God, but because they had been tested by generations of human trial and error. The libertarian belief is that moral codes that have been derived this way are vastly superior to those imposed on us by governments.
You make it sound almost as if Kirk were himself a libertarian. Not so. Most libertarians seem to think that individuals are completely independent units, whose selfish and uncoerced actions will somehow work out magically to everyone's benefit in the end. Kirk valued custom and tradition for their stabilizing effect and thought societies were organic entities. He was fond of everything traditional, old, and customary. His idea that governments are instituted by God doesn't fit too well with your theory. That idea actually traces back to the New Testament, as does most conservative thinking, like the idea that man should have freedom and dignity. That's why free societies and limited government evolved only in the Christian West, not under Islam or in the Far East.