If that ever were to happen, then "the West" would have descended down to the savage, animal way of thinking which you attribute to the extremist Muslim world.
In other words, if that happened, the West would no longer be the West. It would become an unrecognizable perversion of something which no longer exists.
Part of being a member of Western humanity means being humane, even merciful. Such characteristics are what separate us from the animals we oppose. If you're saying the only solution is to destroy ourselves by becoming that which we hate, then maybe a more "classical" destruction of the West is to be preferred. At least then, in losing, we would still be what we are as we meet our end.
I do tend to agree with you regarding the import of this conflict. It's not something which can be overlooked, swept aside, or dealt with cursorily. I am absolutely convinced that if the Muslim world does not purge itself of these extremist elements from within, then the solution will finally be imposed from the outside. And that means their obliteration, a destruction as complete as that which the Nazis ultimately experienced.
And yet, there are still Germans in the world, despite the horrendous ideology which they for a time embraced. Germans have rejected Nazism, but they certainly still embrace the murderous abomination called socialism, to whatever degree.
I believe that a similar process will take place within the Muslim world, since the only alternative will be their annihilation. Eventually, whatever elements of Islam which are not obliterated will become "watered down" to the point that they are more compatible with civil world society.
Thus, I don't believe that we should be hysterically advocating genocidal executions of all fighting age Palestinian males, for instance. Not only is the sentiment patently un-Christian, but it will only serve to drive more moderate elements into the arms of extremists, and that only makes them stronger and our task more difficult.
Moderate, civilized Muslims do exist: just go down to your local convenience store for an example. These people want to live their lives in peace, and otherwise be left alone, just like you and I do.
Just as it will always be legal to own a copy of Mein Kampf, it will always be legal to own a copy of the Koran, and thus there will always be some who follow its teachings to whatever extent.
In summary, I don't believe that the Western (Christian, if you will) solution to the Islamic extremism problem will ever take such an absolutist form, because if it did, we would be no better than our enemies, and would indeed become indistinguishable from that which we hated. And that is not victory.
I can't help but think that, somehow, some way, Christ will lead us down a different path, perhaps one which we can't see yet. But if we go down the savage absolutist path, it will not be Christ who leads us.
Who knows, maybe He will return in time to preempt such a crisis?
Regardless, once that particular problem is solved, we will still have this annoying totalitarian Marxism thing to deal with in the (ostensibly) civilized world.
And, IMHO, that problem is ultimately going to make Islamic extremism pale in comparison.
Have a nice day.
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.