I agree with all but your conclusion, or I guess solution, to the problem these people pose.

Your solution will lead us to doom and destruction. To being no better than them.

And why risk keeping them alive any longer than absolutely necessary? All we end up doing is risk their escape to fuel petty revenge and to "feel better" as if it will actually give you that feeling you're looking for. It is objectively just worse and more risky for the rest of the children of the world than killing them quickly and without delay.