WRT the OP's thesis, I think some folks are missing the forest for the jihadi propaganda.
We are in the ME/Muslim world today. We were there yesterday, we'll be there tomorrow. (Historically speaking.)
We've (the USA) been there since the birth of the nation (Barbary Pirates).
[Western Civ has been in the ME since before Christ, given that Christianity (and therefore Judaism) are fundamental building blocks of Western Civ. Western Civ has been menaced by Islam since it broke out of the Arabian peninsula in the 8th Century.]
The formula goes like this:
1. Nutjob Muslims take the Koran, Haditha, and contemporaneous histories of Mohammed seriously.
2. NJs start to threaten and/or destroy American interests in the name of their god.
3. America takes it in the shorts for a while and finally gets fed up.
4. America sends armed forces to kill the jihadi scum and occupy for more or less time.
5. American armed forces leave and eventually new idiots begin to take the Koran, Haditha, and contemporaneous histories of Mohammed seriously...
Now, I have a dark view of human nature and expect that the Western Civ will have to periodically slap down the savages, drain the swamp, push back the verge, whatever. Western Civ will do so until it commits civilizational suicide or the eschaton, whichever comes first.
But, what if there were other means to kill back the jihadi weeds with less risk to civilized peoples? Would not that be better than shipping our men & women over to some dunghill country to kill goat-humping fools with visions of martyrdom dancing in their heads?
Something like the Iran/Iraq war (which kept both from getting too frisky with the West), distributed enough draw in the jihadis and turn them into fertilizer. Like a regional bug zapper. Or, maybe just at the country level, pitting domestic extremist vs domestic extremist, sort of a Mohammedian Spy vs Spy.
The Muslim world is split enough, crazy enough, and paranoid enough that such an indirect approach is likely to keep them occupied...and make the direct kill-and-accupy approach less likely.