If you doubt this... then just read some history of labor rights in the world. Absolutely horrifying things were done by the law in the name of suppressing unionization all around the US and abroad.
Plus, some protests turn ugly. We saw this in Seattle and elsewhere during the BLM protests. Some protestors engage in property crimes and violence, granting an air of legitimacy to a strong police response.
[1]: https://gothamist.com/news/city-argues-nypd-had-no-special-d...
tl;dr: having a "chilling effect" is, according to SCOTUS, often (but not always) the same thing as "actively suppressing" freedom of speech.
The answer to 'The police are indiscriminate and unaccountable in their use of violence against the public' always seems to be 'Employ even more indiscriminate and unaccountable violence against the public.' It's almost like that's the only response these institutions are capable of.