Se7en is basically an allegory about terrorism. John Doe has a particular worldview and a plan and he is willing to die to see enacted. By killing John Doe you become part of his plan and give him more legitimacy than you otherwise would have.

This is what makes John Doe particularly sinister as a villain. You accomplish nothing by killing him. In fact he wants nothing more than for you to kill him because it legitimizes him further.

However at least in American understanding of law enforcement and warfare, you can only "win" by dominating the battle-space, never mind the fact you just yourself embroiled in a protracted war that's eating up everything with no end in sight.

Nobody ever asks what creates a John Doe, the conditions that made him able to exist in the first place. There is only more John Does who keep on propping up fueled by the death of the previous John Doe or the same root conditions that created the original.

Se7en is a nihilistic film when it comes to policing. It posits that the police are not equipped to handle the conditions that fuel violence and thus will only end up perpetuating it. They have no option but to engage.

From it's opening scenes when Somerset asks "Did the kid see" only to have another detective chew him out for even bothering to have a little empathy, to Mills's hair trigger temper playing right into John Doe's plan it posits that policing will always be a reactive force-

ill equipped to even begin to ask the question of what's creating this violence in the first place. John Doe wouldn't thrive in a good environment. The city itself is decrepit and falling apart. Violence exists in everyday life and nothing is being done about the root cause.

And that's the perfect nest for John Doe and his ideology. The apathy that allowed things to get this bad is what allows him to thrive.