It's a shock to the system to force people to dig deep in their daily lives and recognize what principles they aspire to and believe are important.
You could try to make the case that civil rights in the U.S. during the 1960s could have been better served by threats and violence, but public sympathy would have never come around and I believe things would be even worse in places like Ferguson today if not for that.
Winning the hearts and minds of psychopathic militants is a nice recruiting strategy if you want to kill a handful of cartoonists, but its also a death wish for your own broader public aims. You can try to put the genie back in the bottle like we're still in the Dark Ages, but public sentiment knows that's regressively sheer folly -- and acts like this only alienate them even further to social irrelevancy.
I definitely agree, but the problem is that these fundamentalist do not try, or even want to win over the sympathy of the public. What's interesting in this respect, is that the major point of the 9/11 attacks was not only the actual attack and spread of terror, but just as much provocing a counterattack of the US on the muslim world, which again in the minds of the Al-Queada leaders would trigger an uprising and holy war of the borad muslim community.
The horrible thing is, that they actually seem to have succeeded. ISIS would not have been possible without the US wars of Iraq and Afghanistan.
Although I would never call ISIS the broad muslim community, as horrifyingly large as the support they receive might be.