I think this discussion is missing a significant issue: why would a democratic government, of the people, by the people, and for the people, use tear gas? Why do British Bobbies carry batons?

The simplest answer, which is the basis of all police powers of the state: to prevent crimes against persons and crimes against property. Riotous mobs get people hurt, often killed. The businesses proximate to a protest, often small businesses, often under-insured due to cost constraints, are very likely to be severely affected by protests that turn violent. Major corporate storefronts can absorb the cost of damages, but the same damages to a mom-and-pop grocery could be the end of the business, no matter how much they sympathize with the community that is outraged. And let me reiterate what I started with: riotous mobs get people hurt, often killed.

Tear gas vs the baton is a lesser version of the observation by James B. Conant, president of Harvard University, in his autobiography: "To me the development of new and more effective gases seemed no more immoral than the manufacture of explosives and guns. . . I did not see in 1917, and do not see in 1968, why tearing a man's guts out by a high-explosive shell is to be preferred to maiming him by attacking his lungs or skin."