Shooting people and high speed chases are bad tools for apprehending criminals. They are more likely to harm innocent people than criminals. Facing off with "violent and brazen" criminals doesn't change this, but also the fact that crime is down suggests US criminals are in fact, neither more violent nor more brazen than those in areas where police use less destructive methods.
This is not a fact. What is a fact is that many police departments stopped reporting crimes, so there are fewer crimes being reported, not that there are fewer crimes being committed.
There are myriad reasons why, but stemming the upward trend of reported violence makes politicians look better and we all know how honest politicians are.