If it were me, this man never would have had the chance to throw broken glass. When the knife came out, my gun would go off! That's my policy.
For me personally (not law enforcement). It would depend on how far away he was and how quickly I though he could close the distance.
For a law enforcement officer, which has a duty to protect the public, I would agree with your policy. Regardless of if the perp attacks or flees, he has shown himself to be a violent felon who is a danger to society.
Someone could argue that the officer should give the perp a chance to drop the knife before shooting him. If the officer confronts someone and they already had a weapon in their hand, or the pulled it out when confronted, but before they could have reasonably identified that it was law enforcement that was confronting them, then they should be given a chance to surrender.
If they pull out a weapon to threaten law enforcement or after they have been confronted and have identified the police, they made their choice and placed the officer in the situation where they must remove that threat to themselves and others. A person that threatens the police or others with a weapons should not be allowed to flee unless the officers are unable to prevent it without endangering others.
On a parallel note, I'd also consider a car a deadly weapon, and if a perp attempts to flee in a car that person and that car becomes a threat to others. The driver has shown himself to be indifferent about causing others serious injury by taking flight in the car, and the officers should be authorized to ues whatever force is necessary to apprehend that person, including deadly force.