Simply put, it is A nation in rubble causes no trouble and its application is as follows:
I like your doctrine, but many geographic areas arent really nations. The West Bank, for example. Lebanon, for another. Non-terrorists living there are next door to terrorists. Unless they want to uselessly get themselves killed, theres nothing they can do about it. Making non-terrorists more miserable and impoverished wont help us fight terrorism and may add to the problem.
Other countries that arent really countries are China, Russia and Mexico. All have factions that can act as the state can and sell WMDs, missile technology and nerve gas. These factions (sometimes companies, sometimes red generals and sometimes cartels) are so powerful that their own government cant stop them.
Until America comes to the realization that this is so and stops trying to negotiate with nations that dont really exist except as colored areas on the map well be vulnerable to the machinations of powerful but non-responsible special interests who are only out for themselves. We need to develop indigenous sources that can go in and surgically remove the problems. (Of course, then you run into the problem where youre helping one tribe wipe out another tribe, so you cant leave target selection to a Harvard study group.)