To one of your points: “I am absolutely convinced that if the Muslim world does not purge itself of these extremist elements from within.”
Islam cannot be reformed. This is a major Western misconception - thinking Islam is like some version of an Arabic Christianity. Any attempt to reform is heretical and the parties making the attempt oblige all other Muslims to kill them - thus spoke Muhammad.
You also seem to be overlooking the fact that the West fought two very brutal wars and yet somehow remained the West; moreover that somehow fighting a third brutal war will somehow change the West.
So-called “Kinder, gentler” wars fought by one party against a brutal enemy will always be lost.
I think you just fundamentally misunderstand the nature of both Islam and war - which, BTW, are synonymous within Islam.
I'm not overlooking that fact at all. My point is that during neither of those two "very brutal" wars did the West round up all males of fighting age and perform mass executions.
My initial response on this thread was in opposition to the advocacy of just such a tactic.
Thus I maintain my conviction that not doing such things is how we will remain "the West" and continue to occupy the high moral ground.
Anger causes men to do horrendous things, and no side in any war is immune to that impulse. But it should be resisted.