It is true that traditional infantry forces can perform COIN ops pretty well if they're trained and led properly. But I don't see conventional war making a big comeback in the 21st century, certainly not long-term conventional war. So while regular infantry can do the job, it would be easier for a specialized force, and indeed the threat from irregular combatants is far greater today than it is from conventional armies. Why fight with a force that is less than optimized for the threat? So I maintain that it would probably be a pretty good idea for the great powers to go with forces like this.
You're certainly onto something with the idea about hunter/killer forces. The British in Northern Ireland used them as did the French in Algeria (they lost but it was actually a very effective part of their strategy). The "surge" in Iraq was greatly aided by SOCOMs vicious and still very secret campaign of assassination against insurgent leaders. And now in Afghanistan we're seeing Petraeus put a lot of emphasis on causing casualties.
I tried to incorporate that into my idea with the inclusion of airmobile commandos and organic air assets. Doctrinally I would think that these forces could be used in a manner similar to how the Rhodesian Light Infantry regiment operated in the Rhodesian Bush War during the 1970s. They were wondrously effective at destroying guerrilla forces in the bush. Here's a brief description of their methods (it's quite similar to some American airborne operations in Vietnam)
Now, it is true that both the Rhodesians and Americans lost those conflicts, but on an operational level these tactics were quite effective. The idea is to use airmobile elite light infantry sort of as "bird dogs" for heavier fire power. They can be set down in insurgent controlled territory and advance into an area, flushing out unprepared insurgents and, by engaging them, making them visible and vulnerable to airpower of all types. Fireforce-type missions can be made even more effective when recon units are clandestinely inserted into insurgent controlled areas, who call in the airmobile forces when insurgent concentrations are spotted. Nowadays we also have UAVs to do this sort of work. Additionally, these airmobile forces can enter insurgent controlled territory and erect temporary checkpoints on transportation routes or conduct surprise cordon and search operations in populated areas. Should these operations draw insurgent fire, all the better. They've made themselves visible and can be destroyed by firepower from the air or elsewhere. Finally they can conduct more strategic-level raids of the type that the Rhodesian Light Infantry conducted against guerrilla camps in Mozambique and other countries.
Of course, hunter-killer operations are not at all sufficient to quell an insurgency and can even make it worse if civilians are frequently harmed. And these operations need to be planned for the specific circumstances of the war they are in. For example, the FireForce missions that were appropriate and effective in Rhodesia would not have been appropriate or effective in Northern Ireland. But the need for an offensive capability to disrupt insurgent activity and keep them on the defensive remains.
So doctrinally, if this force were to be created and employed, I envision the brigades of infantry securing the most populated areas and routes of transportation. They're the ones that protect and engage with the local population. They build networks of informants, man checkpoints, do development projects, protect elections, etc. All that normal COIN stuff. Outside of areas that are "secured", the hunter-killer teams will operate, taking the fight to the enemy in the manner that I described. I suppose that the idea would be to eventually expand the "secured area" outwards, but that might not be possible without increasing troop numbers indefinitely, depending on the situation.
