UPDATE: Enough of the Hegseth critique, which does dance around the main question. For readers such as myself, with no actual experience in the counterinsurgency arts and practices; and for chain of command enlightenment,Gen. Michael Flynn wrote in Jan. 2010 (with two co-authors); while roughly a year later an alternative study was released. Another year and some weeks later, a third opus was penned, calling counterinsurgency a thing with "Operational Art" in the resume. [UPDATE: "Operational Art" was already a buzzword in 2010, and "counterinsurgency" a cottage industry among war pundits.]
All three original links above are "studies" at the behest of one or another General, or at least the major fingerprints on each seem to be via different Generals; (civilians need not apply nor offer ideas??).
Actually, the second of the three seems to mirror work of a committee, but please recall that the official story of the JFK lone-wolf assassin and the 9/11 commission report each was by committee; so trusting committee work for divergent views to leaven things in a good way is not without risk.
Reading and evaluating such things as those three items without having had any combat or military experience is not an easy task. It is so much easier just to sit back and smugly ridicule Hegseth. He's on FOX obnoxiously posturing a role akin to the guy who sticks out his chin at a bar saying, "Go ahead, give me your best shot, I can take it." The invitation is there, clearly extended.
However, if counterinsurgency is a major part of Pentagon brass tactics, knowing something about what they mean when they speak of it has value in a society ostensibly run by unerring civilian control of armed forces. Even with a General, Mattis, sitting atop the Pentagon pyramid while his General's chair has barely cooled a bit from his having sat a long time in it. Perhaps particularly with such top level upturning of civilian control it is more important to be vigilant. Complacency can forfeit liberty. History has lessons.
FURTHER UPDATE: Apart from absence of physical weaponry in politics, much of politics arguably can be viewed through a counterinsurgency lens. Is there much room for debate that Debbie Wasserman Schultz showed little "Operational Art" in how she and her DNC hangers on and henchpersons countered the Bernie insurgency? She came across as if trying to intercept falling drifting feathers with boxing gloves laced on so tightly she'd not give them up despite clear difficulties.
FURTHER UPDATE: An easy critique of "counterinsurgency doctrine" is that if Hegseth is put forward as a knowledgeable talking head AND trainer of counterinsurgency troops, doom to failure is inherent. Beyond that premise, Hegseth is an apologist, and not a particularly skilled one, while the heart of what U.S. counterinsurgency was, is, and will be might be personified by James Steele, the question being how close really is Hegseth's background to Steele's? A landslide of words and "counterinsurgency" white papers cannot hide the James Steele in current U.S. military practices.
FURTHER UPDATE: With the Hegseth counterinsurgency background, it is a surprise James Steele gets on FOX coverage, no love among the Hegseth corps; while BBC has done a video short excerpt. Full hour-long item.
FURTHER UPDATE: Rand Corp. has a piece of the action, its counterinsurgency think tanking having started before the earlier cited items, Rand publishing in 2011.
Newer items - from this year and the most recent two seem absent in search return lists. Two items dated 2006, here and here.
After Libya unfolded into chaos from its former prosperous autocracy and while Afghanistan poppy production soared and continues, what's been the outlook on counterinsurgency doctrine, say from during the second Obama term and as a policy debate in the 2016 election? An ongoing continual state of war and terror remains, whether ginned up by our nation's Hegseths or real, yet in public propagandizing it has been back burner. "Great again" rhetoric took front burner, with the Bernie insurgency being real despite mainstream media's intent to downplay it.
The progressive insurgency is one for which real hope must be held by anyone believing much of all else has been conjured-up smoke and mirrors.
Last, counterinsurgency against Bannon worked short term for the new autocratic "General Chief-of-Staff," that being so despite Roy Moore as the show-piece of Bannon-Mercer post-resignation MAGA mischief.