You are correct, but I miss the days when cops were better, when they would assess the threat, in their own station, and resolve the issue without having to kill a little girl. Beanbag rounds, tasers, batons, rushing her with shields, locking her in a non-public area until she calmed down, etc etc etc. And yes, I've taken on a person with a knife before. I got a cut on my arm, but I disarmed them before they did any other damage. The cut healed. No scar.
What makes you think that they did not assess the situation?
Had they approached her and she remained stationary, then that would be a time to attempt to talk with her.
Even wielding a knife, if a person remains where they are at a distance from any target, then they are not really a threat to anyone except themselves, unless of course they are an expert knife thrower (yes, such people do exist).
That would be a scenario in which words or other non lethal means could be considered.
But as soon as she moves towards them, she has made herself an imminent lethal threat, and that is all there is to it.
As per your own encounter, I am happy that you came away without serious injury, but I would like to point out that had your assailant cut you under your upper arm, or on your inner thigh, or on your neck, the outcome could have been much different.
Do not underestimate the effectiveness of a cutting edge as a killing weapon.