Really? That again calls into question the idea of qualifying something as "COIN." - Insurgents can try to take over legitimate governments. Insurgents/Irregular forces, do not always have a legitimate case. Algeria in the 1990's and Sierra Leone being good examples - and many others. War is politics. Why assume the Government or existing power structure is always at fault?
Military action can and does force "insurgents" to seek non-violent means. That is the aim, as it is in almost any conflict of that type.
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