It's simple, really, although it appears to have escaped America's Best and Brightest in the 2000s, chief among them GEN. David Petraeus. The architects of COIN from GEN Joseph Gallieni (1849-1916) to David Galula (1919-1967) all wrote about the need to apply a "global approach." The basic idea was that counter-insurgent forces had to undertake a wide variety of activities, with combat operations being only a small portion of them. The rest consisted of a number of tasks associated with administration, development, governance, and politics. During the Cold War they added to the list the need to reforge the social contract and attend to ideology. There had to be a cause.
Decolonization did not change the need for a global approach, but it limited severely the role to be played by the intervening military. Instead of taking upon itself the bulk of the tasks that fall under the label "global approach," the post-colonial force can do no more than conduct combat operations. Most of the rest then falls upon the shoulders above all of the host nation, with the help of multi-national civilian agencies. But it's really the host nation that has to reforge the social contract and make progress with respect to ideology and promoting a national ideal. France's own circa 2013 COIN doctrine states the matter clearly:
As opposed to “pacification” associated with past experiences, COIN aims to establish the conditions that permit the restoration of the social link within a sovereign host nation. The intervention forces do not look to impose an alien order, to conquer and to stay in the host country, but rather to transfer as soon as possible the responsibility for security to autochthonous forces. They only act in support of a local political structure. In any case, it is the indigenous political system that orients and even constrains their action.
What this means, however, is that the success or failure of the campaign depends largely on the host nation. If it makes an earnest effort at the global approach, the campaign theoretically might work. But what if it does not? The results are evident in Mali, as they were in Afghanistan. The most intervening force can do is be as clear-eyed as possible about what is going on, and brutally honest about the chances of success.