Osama bin Laden's mistake?

Terrorism. If he eschewed terrorism and instead hit only military/fed. governmental* targets, would he have generated more sympathy/less hatred? In this scenario, the 9/11 attacks wouldn't have used commercial airliners (unless otherwise empty); imagine if he had moles with access to military planes.
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*Not as good, because it could be argued that certain central gov'tal employees are innocent (even if they are not), creating sympathy for them (or more than they might deserve).