It is a rule written to protect the lowest common denominator of a policeman from his own incompetence.
"Don't pull a gun unless you are going kill someone with it." Assumes that the user is too stupid to escalate their response. Incapable of decent marksmanship. Stupid enough to wait too long to bring their gun to the ready. And not to be trusted to not shoot someone if they have a loaded weapon in their hand. When I investigate something suspicious in one of my properties I do so with my gun in my hand. It provides more time to think, not less. The same practice is true in the U.S. military when dealing with varying levels of threats (not including war). Weapons are selected, armed, and set to fire. Self-defense is always an option, but lethal force is never a must. Somehow the military is able to arm a missile against an aircraft acting in a hostile manner without feeling that they are obligated to then fire it.
The correct response to a person brandishing a knife, sane or crazy, is to pull your weapon and cover them, and assess the situation. When someone is 15-20 feet away with a knife, there is no reason for someone who considers themselves a trained professional to kill them. The police are supposed to be trained professionals, right? Supposed to be more concerned with public safety than their own, right?
Such police action is all the more inexcusable when there is more than one officer present. You're insisting that the person with the knife is going to suddenly leap 20 feet, get missed by three officers, and stab someone.
Again, you and other posters are proving why the public is less and less comfortable with police actions that have more to do with protecting themselves than serving the public.
Far too many LEO's are incompetent with their firearms and instead of providing more training, they are taught to shoot with less provocation. It makes perfect sense that a sane man with a knife might likely put it down if he has a gun pointed at him, thus there is a great reason to point guns at him (even if you don't shoot). For a person have a mental issue, you are their to serve and protect them too. Killing them should be the absolute last option. Your claim that purposely wounding someone isn't an option is silly. You can say that its not guaranteed to be nonlethal, you can say its more difficult, you can say that incompetent people shouldn't attempt it, but to say that its simply not an option for people who are supposed to be trained professionals is just nonsense.
The problem isn't what you don't know, it's what you know that just isn't so.