While the logic is sound, sadly I don't think the Western world (yet) has the gumption to soundly thrash the screaming beards each time they get it into their heads to be Hereos martyrs.
Well, it's kind of the flipside of what the Islamists are doing.
They engage in asymmetrical warfare in an attempt to escalate the situation until their client/sponsor states have no choice but get involved in the great final jihad or whatever. (Which largely fails, because even the worst of their client/sponsor states have heavy investments in the status quo, to go beyond some funding, material supply, and using them as low grade proxy war.)
My idea of an inflammatory CGI movie is well within the means of a private group. It would escalate the Islamists and get our client states involved. That side of it is easier, because the .gov generally has no choice but to respond to security threats such a cartoon/movie would generate.
Plus as Micro pointed out, the Islamists tend to get themselves killed just in the preparatory phase A LOT.