They (the Romans) make a desert, and they call it peace
The trouble is that your course would lead to an expansion of terror and imitators across vast swathes of previously unaffected nations and matches Al Qaeda’s dreams exactly. Witness their delighted attempts to make the tradition Islamic anger points resonate in nations like Indonesia and others traditionally disinterested in the more Middle eastern issues.
The more martyrs we create the stronger Al Qaeda (or imitators) become. Yes, all might be destroyed in the end but it is by no means certain this can be achieved without severe damage and cost which might be avoidable by clever tactics. Sometimes killing is the only way; at other times the same end can be achieved without turning the target into a rallying cry for a wave of new recruits.
“The trouble is that your course would lead to an expansion of terror”
We don’t know that because it’s never been tried. Appeasement doesn’t work - we know because that’s been tried. Neither have the piecemeal attempts to date.
Bottom line - the Islamic terrorists seek global domination just like the Nazis. They will win unless there is a concerted effort to wipe them out.