This only works if you kill everyone, without exception. Which doesn't happen. Even carpet bombing only kills a relatively small percentage of the population. Human beings are really pretty tough -- kind of like cockroaches, pigeons, and sea gulls. And what happens if you don't get them all? This is what happens: you kill some guys wife and kids but miss him. He goes and becomes a dedicated anti-American fighter. He kills some of our guys by sniping, eventually he gets killed. We go bomb some more villages, make more guys just like him.
So why don't we just kill everyone, without exception? Because, surprise, we really do want a functioning country with an oil infrastructure that we can use to:
(a) Strategically offset the Saudis when we get around to them.
(b) Act as a territorial base for our military to do ME power projection. This means having a functioning economy where we don't have to ship everything from the good old USA.
Ergo, we can't just kill everyone. And if we don't just kill everyone, then your strategy would cause more problems than it would solve.