I wished I could find the documentation but I recall during our training that a man with a knife a short distance away (let's say 5 m away) is a greater threat than a man with a gun a long distance away. The gist of it was target prioritization.
Also read that there was some sort of drill that concluded a man with a knife can close the distance of 6.4m in approximately 1.5 seconds. Considering the condition of your weapon (e.g. firing condition, condition 1 = round in chamber ready for BANG!), you could find yourself out of time if you have to pull the slide, sight in and pull the trigger.
Point is if we're talking close distance and a fast moving, hopped up on My Dew or other "things", the guy with the gun's advantage may be negligible especially if they are a shit shot (storm trooper aim. Couldn't hit the broad side of a barn. Lol)
Oh and most def forget all that nonsense about leg shots like you said. If someone coming at me like that, they getting the 3 piece special. 2 to the chest (center mass) and one to the dome.
Oh and I forgot revolver is kind of a different story, too.
Place yourself in the other shoes as well. Everyone knows cops have guns and fire when threatened. What's going through your mind? A knife in your hand, guns pointed at you. At that point, moving closer is the dumbest move, yet they still move in... That kind of mentality needs to be taking the blame. Make a choice, deal with the consequences.
I saw an incident come out of Chicago recently. Two cops in a park, they approach a man after getting a call to check it out. He pulls a knife and the young lady cop was one the receiving end of a few stiff jabs to the belly. And honestly, I think the cops hesitated because of these politics. All it takes is a split second. Even in a fist fight, most people with experience know waiting around for the other to throw the first shot is how you get your ass beat.