In law enforcement, we were taught that incapacitating head shots are an option in a hostage situation, but only when you are close enough and confident enough to take that extremely narrow shot. For most of my career, we carried Sig Sauer .357 semi-automatic pistols with a hammer you could cock for single-action. Moving from the long, heavy double-action first pull to single-action gave a light, short trigger press. That was a good option if the hostage taker and hostage were standing still.
Once the unjust aggressor and the intended victim (citizen or officer) are entangled, grappling, moving, or being moved, the situation changes. At that point, a precise shot is usually no longer a good option. Someone has to close distance and get their hands dirty. A violent separation can involve tackling, shoving, or jerking away with momentum. Even a temporary separation can create the space the legitimate defender needs to deliver incapacitating shots and stop their continuing imminent deadly threat.
The two parties may also separate on their own through pushing, pulling, or maneuvering. When that gap opens, a composed officer or citizen protector can exploit it with one or two well-placed shots. This is not, and cannot be, a mag-dump solution born of panic. Composure under those conditions is usually earned through enough “wild and woolly” experience to see opportunities as the violence develops. If you lack the experience to have and maintain composure, the only other reliable hedge, in my opinion, is to over-develop pure shooting skill so that even a high-volume response remains exceptionally accurate.
Know your adversary and know yourself. Deliberately strengthen the areas where you are weak rather than continuing to polish only the skills that already make you feel competent. Do the hard work necessary to expand your capabilities so those skills run in the background under stress.
Videos show officers making rear, very close, or contact shots to stop the threat. In today’s confused legal environment, especially in dense population centers, you will want as much of the encounter as possible captured on CCTV or doorbell cameras. You don’t get to pick the time and place where ol’ boy breaks bad, so realize these kinds of solutions carry higher risks on the legal battlefield. This isn’t legal advice; I’m not an attorney; I’m simply sharing how I looked at this kind of problem during my career and still do today.
The best solution for almost all of these problems is still early recognition. See what is developing, get ahead of it, and dominate inside the moral, legal, and physical windows of opportunity before the parties become entangled. Once they are locked together, the required solution carries far higher physical risk and will look ugly to anyone who does not understand real violent encounters.