The shoot-first instinct that seems so pervasive among many US police is in stark contrast to law enforcement tactics in other countries. British police, for example deal with a large number of edged-weapons attacks but almost never open fire (they don't generally carry guns). Just as there are countless online videos of trigger-happy US police, there are numerous recorded examples of UK cops intervening in violent situations without firing a shot.
In one 2014 incident, for example, Albuquerque police attempting to arrest a mentally ill man for "illegal camping" opened fire on him with assault weapons when he drew a tiny blade at a great distance from the heavily armed officers. Their approach is summed up by the fact that they then handcuffed him as he lay dying on the ground. A good contrast is a 2015 video of officers in Corby, England wresting a knife from an attacker using only pepper spray and batons at close range.
Comment: One tactic not mentioned: Weeding out the pathological types to keep them from joining the force in the first place. However, considering that police are simply tools of the state and enforcing control is their job, this will likely not happen.