This whole controversy has reminded me a lot of when the Army adopted the Counter-Insurgency Field Manual in Iraq and Afghanistan. A lot of the grunts hated it. At its core, they were being asked (ordered) to give up their tactical advantage in very dangerous situations. Don't point your gun at people, don't shoot unless you're being shot at, don't kill unless it's absolutely necessary, smile and eat with a person you know is going to plant bombs and try to kill you... Troops hated it. It went against everything they'd been taught. Importantly, it also cost people their lives. In those tense, dangerous environments, being slow to resort to lethal force can absolutely get you killed.
However... if you looked at the policy from a different angle, it saved lives and advanced American interests. At the tactical level, it is always right to use overwhelming force. That's how you win quickly, cleanly, and safely. At the macro/strategic level, you don't necessarily want your people winning every single fight- you want to reduce the number of fights. That's what really saves lives in the aggregate and whether you're talking police work or counterinsurgency, it's the end-state you want to get to. You can't build good relationships if you treat every encounter with a community as a potentially lethal situation.
Unfortunately, the macro level policies are never going to be 100% effective. There will always be violent people out there. A lot of the time, our cops and soldiers will be able to recognize this regardless of whether they're in traditional hard-charger mode or if they're playing a more friendly/COIN approved role. Once the initial ID of the situation is made, then under any regime they will respond in roughly the same way (nobody ever has argued that a cop can't or shouldn't shoot someone who is shooting a gun at them.) However, there will be a small subset of cases where the more passive approach means that the bad guy gains enough of a drop on the good guy that the good guy loses a fight (read: dies) that he could have won had he been more aggressive.
It sounds shitty to say that the optimal # of dead cops or soldiers =/ 0, but it's true. I think it's misleading to ask whether a cop's life is more valuable than a criminal's life (or a soldier v an insurgent), because that's only looking at one situation in a much larger pattern. The important point (from a macro level) is that we want our armed representatives on the ground acting in a way that reduces tensions, builds trust, and ultimately reduces violence. Unfortunately, the only way to achieve this is to ask (order) those representatives to -not- always use the maximum level of force, even if it's an appropriate tactical response to a potentially dangerous situation and there's a chance failing to do so gets them killed.
