Yep, this is like how Hitler came to power. If you can create a bogeyman, and convince a bunch of losers that their lives suck only because of that bogeyman, then it gives the losers something to fight for (or rather, become cannon fodder for, or in the case of the mussies, become living explosive shells for).
Even if they wiped Israel off the map, some Imam would whip them up in a jihad about somebody else that is bothering them. The west dealt with fascism in WW2 by bombing the living crap out of most of Europe and hanging the ringleaders. In the Pacific, the Japanese were so fanatical, the allies had to kill almost everyone on the islands they took because the fanatics chose death over surrender. The W.O.T. will never be won as long as the west continues to allow its hands to be tied by political correctness and a "can't we just get along" mentality.