"that mentality is what drives it all: if only we can get enough of these bastards, we’ll win the war" You would have thought they would have learned something from the last couple of failed invasions - you don't win a war with technology. You win it with troops on the ground. This is the Rumsfeld Doctrine in action, and again we'll see it fail.
There are multiple entities involved in the war campaign. Our country's military establishment, our country's military contractors, our citizens, our civilian government. The other country's civilians, military and goverments, Warisitan warlords.
Even on the same "side", a win for one entity doesn't necessarily mean a win for the others. The parties that are immediately controlling the war campaign win by prolonging the war. Imagine the billions spent on drone warfare, on training pilots, software, components, whole careers civilian and military and whole divisions of large corportations devoted to supplying and maintaining the "War on $X" (here $X is "Terror" but replace with "Drugs", "Communism" whatever).
Remember Bush's "Mission Accomplished" banner from his visit to USS Abraham Lincoln during Iraq War is often criticized as the dumbest thing, since for the civilians and those not involved in the war directly it obviously wasn't accomplished. But it was accomplished for those involved in the war because it would ensure increased spending, activity, involvement and churn for years to come.
Going back to the story -- "if only we can get enough of these bastards, we’ll win the war". There is probably not a concerted rational effort to target civilians with the purpose of ensuring a steady future stream of extremism. But I think due to payoffs and contraints existent across the system, that is effectively what is happening. Everyone in the chain has no incentive to stop. They do what they do, everyone is "doing their job". People on the ground get bombed. Children see fathers, sisters, mothers, grandmothers blown to pieces, by drones. They vow to avenge their blood. Drone operators get reports of extremist activities, the do their job. Drones get old, wear out, those that make those, get orders for more drones. Etc.
Imagine a fantastic scenario. You are a CIA drone operator. You've been "flying" and blasting away goat herders for 10 years. That is all you know. You are good at it. That is your life. All of the sudden, all terorists are finished. They just pack up and go home. No more extremism. What does that mean for you? What's next? Go study Hungarian to hopefully get post as "a cultural attache" at the embassy there. Start cutting grass around Langley's HQ?