A while back I read that it's pretty hard to stop a man who has a knife if he's nearby. If they charge you then you only have a couple seconds to react. Bullets don't kill immediately, especially when you aim for the center of mass.
Also, it's nigh impossible to draw your gun and shoot a man who is charging you with a knife, so that explains the gun pulling on people carrying knives. Not saying it's right, but it is what it is.
Non lethal takedowns of armed people are hard as well, requiring careful coordination.
On the other hand, I read a rather convincing article from an Iraq war veteran who hypothesized that if cops stuck their own necks out a little bit more, even at the cost of their own safety, then public outreach would be a lot better. The man drew these conclusions from his own anecdotes working with Iraq's populace on his tours.
Food for thought, I suppose.
