The use of force works only for containing the activities of currently extant extremists, if even that. The UK plus its local supporters had a varying-intensity war going on with North Irish radicals for closer to a century, and in the end only really managed to get any progress at the negotiation table. Various breeds of repressive and authoritarian regimes, able to operate with far more ruthless methods than democratic ones, have on the whole consistently failed to eliminate sufficiently dedicated armed opposition groups - the ETA survived Franco, for example, and the Algerian governement hasn't made any real headway against its local gunmen. During the asymmetrical Algerian War the methods adopted by the French that at least seemed to work were then so vicious and morally repugnant public pressure eventually forced them to bail out...

Basically, if all killing one zealot manages is to buy a brief respite before the next guy in queue fills his boots (now wiser from the demise of his late colleague), all you're managing to do is buy time. You're just fighting a holding action. Well, fighting holding actions is often very necessary and all, but they won't get you very far unless you can do something more meaningful too - and if the evidence thus far is to judge by, invading countries and gunfights with zealots don't quite fulfill the criteria of "meaningful".
Put this way: the loose, nebulous networks that can for brevity be called "al-Qaeda" for short are not only managing to keep the Americans and some others very preoccupied, at enormous financial cost, in Iraq and Afghanistan and presumably sundry other, less well-known, locales; they could effect the Barcelona and Londond bombings on the side too...