It's not just lethality, but it's also not just the way police respond, because it's not one or the the other. If you don't agree that the lethality of the weapon is a significant input to whether or not a dangerous outcome is more likely, we can't have a serious conversation.
Of course the weapon in question is also a variable, but I by far the biggest variable is police behavior in the US, where it seems every situation calls for force escalation and solving the matter at hand with a full-on assault of some sort.
I think you're right that escalating behavior is a significant variable. But I think that's a very tough thing to change. It may be that the low hanging fruit consists in changing the equipment rather than the culture. But I don't disagree with you in the big picture.
Anyway, I'll be careful not to assume your comments are attempting to be responsive to the things they reply to when I see them in the future, to prevent my misunderstanding.
In most (northern) European countries the response to somebody brandishing a knife would be to set up a perimeter around that person, rather than directly engage them. Only as a last resort would you resort to violence. Instead you try to tire them out.
By comparison, the American police response would be to immediately subdue the person with any force necessary.