My wife is from Russia, and she agrees with you. Russians are much more about keeping order than free speech, and she wants to see armed troops on the street keeping her safe.
In the US, Police throw tear gas and beat protesters with clubs, protesters throw fireworks and break windows. It is an agreed upon battle, fought mostly by kids who are mostly 18-25 (and mostly white in my neighborhood).
Shooting would be a big escalation, which is not commonly done in the US, and could be answered with bombs like the Haymarket incident in 1886, or even more protests and changes in politics leading to like happened after Kent State in 1970.
As a teenager I did some of this sort of thing in protest against my potential draft notice. As a Border Patrol Agent, we occasionally used tear gas to break up crowds, so I can see it from both sides.I like the RCMP policy on shooting felons. It says that you do not shoot to kill, you shoot to stop. The need to stop a person must be so great that it does not matter if he dies as a result.