War against terrorists is hard, but war against a fielded army is pretty straightforward. ISIS has command and control, vehicles and headquarters as well as convoys and masses or groups of fighters occupying villages or cities where the locals are willing to point them out to a rescuing expeditionary force.
As long as the receiving Western army manage to find zero terrorist prisoners alive to round up, they can defeat the enemy! There'll be none to return to Europe! OTOH, in previous years, trying to identify Shiite terrorists in their own villages was near impossible. The same with identifying Hamas fighters in Gaza "Mau Mau" in Kenya over 50 years ago!
But in the case of ISIS, they mostly occupy land that they are not
native to and they have treated the locals with contempt and terror.
ISIS has terrorized populations it took over and so they will be pointed out to any invading army who comes with strength , food, rebuilding and enough funds to get their lives back!
An air campaign cannot do that as ISIS fighters can retreat and then return. In a military sanitation of the area, the occupying terrorists would be shot as they resisted the oncoming forces and that solves the problem. This would be a shoot to kill campaign or it would have no practical advantage. Chasing them elsewhere serves no purposes and in fact worsens the situation. Essentially anyone trained for terrorist activity has to be segregated and those that fight killed.
Totally doable! Remember, in the Desert storm campaign and in the Israeli-Egyptian Sinai war, defeated armies were simply allowed to escape. However, against an ideologically committed force, if they are engaged, the only reasonable outcome is their liquidation as such folk on not likely to be rehabilitated by any known persuasive argument.
There's no possible approach to stopping a determined, idealogcally-bound, fanatic and well-financed insurgency except by boots on the ground. wishing to be reasonable and restrained simply kicks the can down the road. I do not expect Canada to take any lead in such a war unless a flock of squealing pigs flies over my building at the same time!
There's another approach and that is simply conceding territory to them, paying them homage and recognizing their government. It's called appeasement, but in a practical sense, if ISIS would accept it, it is likely to be a temporary tactical decision and not a strategic policy change in their quest for hegemony.
Asher