This is exactly what is needed in the Islamic world.
Whether or not the inhabitants of those benighted countries turn out to be "deeply grateful" is beside the point.
It will be by far the best thing for the rest of the world, and
There is no excuse for the toleration of an imperialistic, tyrranical theocracy by the civilized world any more than the toleration of Naziism or Japanese imperialism.
Islam is imperialistic.
Islamic apologists like to sweep this little fact under the rug.
Demand unconditional surrender. Sweep away the cultural legacy of centuries, and impose an American-style constitution, with guarantees of freedom of speech, freedom of religion (including the freedom to convert to religions other than Islam), separation of religion and state, and women's suffrage. If the subjugated population objects--too bad. Open these countries up to missionaries. Convert them from the imperialistic, intolerant, war-like, tyrranical religion of Islam to some other religion--any other religion. Give Islam the respect it deserves--none.