>people who, make no mistake, want to destroy our way of life.
Don't be melodramatic - for the most part they don't even know what our way of life is, except for the part that involves spending the better part of a century manipulating their domestic politics for our own ends - overthrowing legitimate democracies, installing sadistic dictators, selling them powerful weapons, etc. And honestly I'd rather like to destroy that part of our way of life myself, I just don't think it can be done via militant action.
For the most part they just want to drive out the foreign devils that are slaughtering civilians and raining death from above, whereas the warlords calling the shots probably secretly love having the foreign devils around giving them legitimacy and bolstering recruitment numbers to leverage in their domestic power struggles. Anything they know about our "way of life" is going to be the same sort of racist caricatures that pervaded US media during WWI and II - propaganda designed to dehumanize the enemy to bolster support for the domestic warmongers.
There is no doubt the occasional extremist who actually would like to destroy our way of life, but without a vast support structure they're just another random terrorist - maybe they manage to take out a few hundred people, maybe even a few thousand - tragic, but statistically insignificant - you chances of dieing in a car crash are much better. And if they do have the vast support structure, then it becomes a business, and like any institution its primary goal becomes self-perpetuation - not something usually furthered by picking fights with opponents that have you vastly outmatched. Though admittedly occasionally you get an Al Qaeda situation, where a crumbling institution deliberately provokes a dragon in order to give themselves a new patina of relevancy rather than fade gracefully into obscurity.
Meanwhile, virtually every "terrorist plot" interrupted in the last decade plus has been initiated by agent provocateurs working for the FBI, etc. *Maybe* you could argue that they're trying to "weed out the bad apples", but the available evidence looks a lot more like they're creating the very threat they're using to justify their ever-expanding authority.