The point is slightly to prevent a thing from happening, but mostly to provoke a massive government overreaction and make it lose face. Such as in this case where a woman was arrested for speaking her opinion at a city meeting.
She was arrested for making an off-topic opinion. Someone delivering a rant about abortion on a city council meeting would likewise be removed.
I don't see a government losing face, I see a bunch of online commenters demonstrating they don't understand that city council meetings have rules.