I ain't buying.

COIN strategy, operations and tactics "ain't my department"; but some conclusions raise policy issues - so, IMO.

Rand
First, policing and intelligence should be the backbone of U.S. efforts. In Europe, North America, North Africa, Asia, and the Middle East, al Qa’ida consists of a network of individuals who need to be tracked and arrested. This would require careful work abroad from such organizations as the Central Intelligence Agency (CIA) and Federal Bureau of Investigation (FBI), as well as their cooperation with foreign police and intelligence agencies.
No argument about co-operation, etc. between CIA, FBI and their external equivalents (subject to standard caveats; e,g., "there are friendly nations, there are no friendly intelligence agencies" - but "we can co-operate, so to speak."). I object to "arrest" as the magic bullet.

With AQ (as with any adversary), there are three basic, non-exclusive paths:

(not a quote - just to set it out)

1. Convert (difficult to do for hard-core AQ)

2. Contain (arrest & prosecution is one aspect of this path - so, within my department as to that)

3. Kill (in other persons' departments).
All three paths should be pursued - based on specific METT-TC, as the military guys say.

Rand
Second, military force, though not necessarily U.S. soldiers, may be a necessary instrument when al Qa’ida is involved in an insurgency. Local military forces frequently have more legitimacy to operate than the United States has, and they have a better understanding of the operating environment, even if they need to develop the capacity to deal with insurgent groups over the long run. This means a light U.S. military footprint or none at all.
No argument, in general, about the first sentence - economy of force is good - except when you get your neck chopped off because there has been too much economy. The issue is the application of the necessary force at the key application point.

The rest of it - Tora Bora; the ISI and the Pakistan border crossings, etc., come to mind as contra examples.

True, that a light or no US military footprint gives us fewer international law problems; but that cannot be the determining factor.

Rand
Religious terrorist groups take longer to eliminate than other groups .... Religious groups rarely achieve their objectives. No religious group that has ended achieved victory since 1968.
Probably some truth there - if the fanatics are not close in beliefs (and practices) to a majority of the target population.

Fanatics are "integral rigidists" (in the sense used in systematic theology) - all their beliefs and practices have to be accepted, or (they believe) their system will fall apart. So, the Taliban became disliked; as also AQ in Anbar (about which others here have written).

Perhaps, that is the basic weakness of the extreme Salafist supremacists. I doubt whether their defeat will occur in my lifetime.