It's difficult to track down threats, which is the primary means of jawboning, and courts often okay with them, despite the significant conflict with the first amendment. There are many cases of it becoming public though, showing how prevalent it is. It was the primary concern in the Twitter Files (https://en.wikipedia.org/wiki/Twitter_Files) and in the Backpage.com, LLC v. Dart case, (https://law.justia.com/cases/federal/appellate-courts/ca7/15...) the Sheriff in Cook County Illinois tried to follow through with the threat, but was overturned by the courts, who tend to have a much stronger response to follow-through than threat itself, despite most of the effectiveness coming from threats.

Also, politicians are constantly threatening to revoke section 230 of the communications decency act, without which hosting any kind of user-generated content, from forums to video streaming to social media, would be effectively impossible in the US, because everything posted would need to be censored before ever being displayed.