Just because it works, doesn’t mean it’s right. Look, I hate Islamic terrorists, and I’m not at all fond of Islam in general, radical or otherwise, but surely there should be some limits as to what is allowed in war? Sherman (and especially the camp followers that he allowed to hang around) hurt a heck of a lot of more people than just enemy combatants. Do we really want to see non-terrorist Middle Easterners attacked and their land destroyed, just so long as actual terrorists are hurt too? What do you really think the end result of that would be? A whole lot more terrorists seeking revenge for their mothers’ deaths and sisters’ rapes coupled with a never-ending occupation, I would imagine.
I don't believe that Muslims are an inferior people, so I tend to think that they would react like anyone else... Southerns after Sherman, for example.
And considering that your scenario didn't pan out then, why would it pan out now?
War is hell... and as long as civilians are sheltered from that hell, they'll work for and call for war. Expose them to it and all the talk goes out the window.
Furthermore, wars only ever really end when one side is thoroughly shown to be defeated. When the citizenry are made to realize that they really did lose, then there no mistaken belief that the losing side could have really won, for the evidence against it is all around.
Just look at Germany and Japan after WWII. Cities in rubble, starvation, and massive internal displacement. There was no way the German/Japanese citizenry was going to claim that the allies simply used dirty tricks to occupy their country. Unlike what we see with our nice, sanitized, 'precise' wars of today.